{"id":562,"date":"2022-08-17T02:49:53","date_gmt":"2022-08-17T02:49:53","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=562"},"modified":"2024-02-21T06:34:11","modified_gmt":"2024-02-21T06:34:11","slug":"ncert-solutions-class-6-maths-chapter-11-algebra-ex-11-5","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-11-algebra-ex-11-5\/","title":{"rendered":"NCERT Solutions Class 6 Maths Chapter 11 Algebra Ex 11.5"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">NCERT Solutions Class 6 Maths<\/span><\/strong><\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">Chapter &#8211; 11 (Algebra)<\/span><\/strong><\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 6 Mathematics <strong>Chapter &#8211; 11 Algebra <\/strong>Exercise 11.5 has been provided here to help the students in solving the questions from this exercise.<\/span><\/p>\n<h4 id=\"chapter-11\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span id=\"Chapter_11_Algebra\" style=\"color: #000000;\">Chapter 11: Algebra<\/span><\/strong><\/span><\/h4>\n<ul>\n<li><span style=\"font-family: georgia, palatino, serif;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-11-algebra-ex-11-1\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 6 Maths Exercise &#8211; 11.1<\/a><\/span><\/li>\n<li><span style=\"font-family: georgia, palatino, serif;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-11-algebra-ex-11-2\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 6 Maths Exercise &#8211; 11.2<\/a><\/span><\/li>\n<li><span style=\"font-family: georgia, palatino, serif;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-11-algebra-ex-11-3\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 6 Maths Exercise &#8211; 11.3<\/a><\/span><\/li>\n<li><span style=\"font-family: georgia, palatino, serif;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-11-algebra-ex-11-4\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 6 Maths Exercise &#8211; 11.4<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">Exercise &#8211; 11.5<\/span><\/strong><\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>1. State which of the following are equations (with a variable). Give reason for your answer. Identify the variable from the equations with a variable.<br \/>\n<\/strong>(a) 17 = x + 17<br \/>\n(b) (t \u2013 7) &gt; 5<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(c) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{2}\" alt=\"\\frac{4}{2}\" align=\"absmiddle\" \/> = 2<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(d) (7 \u00d7 3) \u2013 19 = 8<br \/>\n(e) 5 \u00d7 4 \u2013 8 = 2x<br \/>\n(f) x \u2013 2 = 0<br \/>\n(g) 2m &lt; 30<br \/>\n(h) 2n + 1 = 11<br \/>\n(i) 7 = (11 \u00d7 5) \u2013 (12 \u00d7 4)<br \/>\n(j) 7 = (11 \u00d7 2) + p<br \/>\n(k) 20 = 5y<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(l) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3q}{2}\" alt=\"\\frac{3q}{2}\" align=\"absmiddle\" \/> &lt; 5<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(m) z + 12 &gt; 24<br \/>\n(n) 20 \u2013 (10 \u2013 5) = 3 \u00d7 5<br \/>\n(o) 7 \u2013 x = 5<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solutions:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(a)\u00a0An equation with variable x<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(b) An inequality equation<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(c) No, it\u2019s a numerical equation<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(d) No, it\u2019s a numerical equation<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(e) An equation with variable x<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(f) An equation with variable x<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(g) An inequality equation<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(h) An equation with variable n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(i) No, it\u2019s a numerical equation<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(j) An equation with variable p<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(k) An equation with variable y<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(l) An inequality equation<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(m) An inequality equation<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(n) No, it\u2019s a numerical equation<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(o) An equation with variable x<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>2. Complete the entries in the third column of the table.<\/strong><\/span><\/p>\n<div class=\"table-responsive\" style=\"text-align: justify;\">\n<table class=\"table table-bordered\" style=\"width: 60%;\">\n<tbody>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>S.No<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Equation<\/strong><\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Value of variable<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Equation satisfied<br \/>\n<\/strong><strong style=\"text-align: center; font-size: inherit;\">Yes \/ No<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(a)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10y = 80<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">y = 10<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(b)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10y = 80<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">y = 8<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(c)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10y = 80<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">y = 5<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(d)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">4l = 20<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">l = 20<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(e)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">4l = 20<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">l = 80<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(f)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">4l = 20<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">l = 5<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(g)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">b + 5 = 9<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">b = 5<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(h)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">b + 5 = 9<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">b = 9<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(i)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">b + 5 = 9<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">b = 4<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(j)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">h \u2013 8 = 5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">h = 13<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(k)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">h \u2013 8 = 5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">h = 8<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(l)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">h \u2013 8 = 5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">h = 0<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(m)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p + 3 = 1<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p = 3<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(n)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p + 3 = 1<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p = 1<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(o)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p + 3 = 1<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p = 0<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(p)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p + 3 = 1<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p = -1<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(q)<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p + 3 = 1<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p = -2<\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solutions:<\/strong><\/span><\/p>\n<table style=\"width: 76.3642%;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>S.\u00a0No.<\/strong><\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Equation<\/strong><\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Value of variable<\/strong><\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Equations satisfied<br \/>\nYes \/No<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(a)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10y = 80<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">y = 10<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">No<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(b)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10y = 80<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">y = 8<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Yes<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(c)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10y = 80<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">y = 5<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">No<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(d)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">4l = 20<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">l = 20<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">No<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(e)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">4l = 20<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">l = 80<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">No<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(f)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">4l = 20<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">l = 5<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Yes<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(g)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">b + 5 = 9<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">b = 5<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">No<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(h)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">b + 5 = 9<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">b = 9<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">No<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(i)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">b + 5 = 9<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">b = 4<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Yes<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(J)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">h \u2013 8 = 5<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">h = 13<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Yes<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(k)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">h \u2013 8 = 5<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">h = 8<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">No<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(l)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">h \u2013 8 = 5<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">h = 0<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">No<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(m)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">P + 3 = 1<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p = 3<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">No<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(n)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p + 3 = 1<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p = 1<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">No<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(o)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p + 3 = 1<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p = 0<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">No<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(P)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p + 3 = 1<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p = -1<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">No<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.99998%;\" width=\"35\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(q)<\/span><\/td>\n<td style=\"text-align: center; width: 22.9545%;\" width=\"89\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p + 3 = 1<\/span><\/td>\n<td style=\"text-align: center; width: 32.3179%;\" width=\"78\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">p = -2<\/span><\/td>\n<td style=\"text-align: center; width: 100.87%;\" width=\"84\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Yes<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(a)\u00a0<\/strong>10y = 80<br \/>\ny = 10 is not a solution for this equation because if y = 10,<br \/>\n10y = 10 \u00d7 10<br \/>\n= 100 and not 80<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(b)<\/strong> 10y = 80<br \/>\ny = 8 is a solution for this equation because if y = 8,<br \/>\n10y = 10 \u00d7 8<br \/>\n= 80<br \/>\n\u2234 Equation satisfied<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(c)<\/strong> 10y = 80<br \/>\ny = 5 is not a solution for this equation because if y = 5,<br \/>\n10y = 10 \u00d7 5<br \/>\n= 50 and not 80<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(d)<\/strong> 4l = 20<br \/>\nl = 20 is not a solution for this equation because if l = 20,<br \/>\n4l = 4 \u00d7 20<br \/>\n= 80 and not 20<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(e)<\/strong> 4l = 20<br \/>\nl = 80 is not a solution for this equation because if l = 80,<br \/>\n4l = 4 \u00d7 80<br \/>\n= 320 and 20<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(f)<\/strong> 4l = 20<br \/>\nl = 5 is a solution for this eqaution because if l = 5,<br \/>\n4l = 4 \u00d7 5<br \/>\n= 20<br \/>\n\u2234 Equation satisfied<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(g)<\/strong> b + 5 = 9<br \/>\nb = 5 is not a solution for this equation because if b = 5,<br \/>\nb + 5 = 5 + 5<br \/>\n= 10 and not 9<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(h)<\/strong> b + 5 = 9<br \/>\nb = 9 is not a solution for this equation because if b = 9,<br \/>\nb + 5 = 9 + 5<br \/>\n= 14 and not 9<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> b + 5 = 9<br \/>\nb = 4 is a solution for this equation because if b = 4,<br \/>\nb + 5 = 4 + 5<br \/>\n= 9<br \/>\n\u2234 Equation satisfied<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(j)<\/strong> h \u2013 8 = 5<br \/>\nh = 13 is a solution for this equation because if h = 13,<br \/>\nh \u2013 8 = 13 \u2013 8<br \/>\n= 5<br \/>\n\u2234 Equation satisfied<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(k)<\/strong> h \u2013 8 = 5<br \/>\nh = 8 is not a solution for this equation because if h = 8,<br \/>\nh \u2013 8 = 8 \u2013 8<br \/>\n= 0 and not 5<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(l)<\/strong> h \u2013 8 = 5<br \/>\nh = 0 is not a solution for this equation because if h = 0,<br \/>\nh \u2013 8 = 0 \u2013 8<br \/>\n= \u2013 8 and not 5<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(m)<\/strong> p + 3 = 1<br \/>\np = 3 is not a solution for this equation because if p = 3,<br \/>\np + 3 = 3 + 3<br \/>\n= 6 and not 1<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(n)<\/strong> p + 3 = 1<br \/>\np = 1 is not a solution for this equation because if p = 1,<br \/>\np + 3 = 1 + 3<br \/>\n= 4 and not 1<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(o)<\/strong> p + 3 = 1<br \/>\np = 0 is not a solution for this equation because if p = 0,<br \/>\np + 3 = 0 + 3<br \/>\n= 3 and not 1<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(p)<\/strong> p + 3 = 1<br \/>\np = -1 is not a solution for this equation because if p = \u2013 1,<br \/>\np + 3 = -1 + 3<br \/>\n= 2 and not 1<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(q)<\/strong> p + 3 = 1<br \/>\np = -2 is a solution for this equation because if p = -2,<br \/>\np + 3 = -2 + 3<br \/>\n= 1<br \/>\n\u2234 Equation satisfied<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>3. Pick out the solution from the values given in the bracket next to each equation. <\/strong><strong>Show that the other values do not satisfy the equation.<br \/>\n<\/strong>(a) 5m = 60 (10, 5, 12, 15)<br \/>\n(b) n + 12 (12, 8, 20, 0)<br \/>\n(c) p \u2013 5 = 5 (0, 10, 5 \u2013 5)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(d) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{q}{2}\" alt=\"\\frac{q}{2}\" align=\"absmiddle\" \/> = 7 (7, 2, 10, 14)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(e) r \u2013 4 = 0 (4, -4, 8, 0)<br \/>\n(f) x + 4 = 2 (-2, 0, 2, 4)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solutions:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(a) 5m = 60 (10, 5, 12, 15)<br \/>\n<\/strong>For m = 10, LHS = 5 x 10 = 50, RHS = 60 <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 m = 10 is not the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For m = 5, LHS = 5\u00d75 = 25, RHS = 60 <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 m = 5 is not the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For m = 12, LHS = 5 x 12 = 60, RHS = 60<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS = RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 m = 12 is the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For m = 15 LHS = 5 x 15 = 75, RHS = 60<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 m = 15 is not the solution of the equation<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(b) n + 12 = 20 (12, 8, 20, 0)<\/strong><\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For n = 12, LHS = 12 + 12 = 24, RHS = 20<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 n = 12 is not the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For n = 8, LHS = 8 + 12 = 20, RHS = 20<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS = RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 n = 8 is the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For n = 20, LHS = 20 + 12 = 32, RHS = 20<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 n = 20 is not the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For n = 0, LHS = 0 + 12 \u2013 12, RHS = 20<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 n= 0 is not the solution of the equation<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(c) p \u2013 5 = 5 (0, 10, 5, -5)<\/strong><\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For p = 0, LHS = 0 \u2013 5 = -5, RHS = 5<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 p = 0 is not the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For p = 10, LHS = 10 \u2013 5 = 5, RHS = 5<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS = RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 p = 10 is the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For p = 5, LHS = 5-5-0, RHS = 5<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 p = 5 is not the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For p = 5, LHS = 5 \u2013 5 = 0, RHS = 5<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 p = -5 is not the solution of the equation<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(d) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{q}{2}}\" alt=\"\\mathbf{\\frac{q}{2}}\" align=\"absmiddle\" \/>\u00a0= 7 (7, 2, 10, 14)<\/strong><\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For q = 7, LHS = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{2}\" alt=\"\\frac{7}{2}\" align=\"absmiddle\" \/>\u00a0, RHS = 7<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 q = 7 is not the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For q = 2, LHS = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{2}\" alt=\"\\frac{2}{2}\" align=\"absmiddle\" \/>\u00a0= 1, RHS = 7<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 q = 2 is not the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For q = 10, LHS = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{10}{2}\" alt=\"\\frac{10}{2}\" align=\"absmiddle\" \/>\u00a0= 5, RHS = 7<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For q = 14, LHS = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{14}{2}\" alt=\"\\frac{14}{2}\" align=\"absmiddle\" \/>\u00a0= 7, RHS = 7<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS = RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 q = 14 is the solution of the equation<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(e) r \u2013 4 = 0 (4, -4, 8, 0)<\/strong><\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For r = 4, LHS = 4 \u2013 4 = 0, RHS = 0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS = RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 r = 4 is the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For r = -4, LHS = -4 \u2013 4 = -8, RHS = 0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 r = -4 is not the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For r = 8, LHS = 8 \u2013 4 = 4, RHS = 0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For r = 8 is not the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For r = 0, LHS = 0 \u2013 4 = \u2013 4, RHS = 0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 r = 0 is not the solution of the equation<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(f) x + 4 = 2 (-2, 0, 2, 4)<\/strong><\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For x = -2, LHS = -2 + 4 = 2, RHS = 2<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2013 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 x = -2 is the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For x = 0, LHS = 0 + 4 \u2013 4, RHS = 2<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 x = 0 is not the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For x = \u2013 2, LHS = -2 + 4 \u2013 6, RHS = 2<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 x = 2 is not the solution of the equation<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">For r = 4, LHS = 4 + 4 = 8, RHS = 2<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, LHS \u2260 RHS<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 x = 4 is not the solution of the equation<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>4. (a)Complete the table and by inspection of the table find the solution to the equation m + 10 = 16.<\/strong><\/span><\/p>\n<div class=\"table-responsive\" style=\"text-align: justify;\">\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">m<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">1<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">2<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">3<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">4<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">6<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">7<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">8<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">9<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">m + 10<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(b) Complete the table and by inspection of the table, find the solution to the equation 5t = 35<\/strong><\/span><\/p>\n<div class=\"table-responsive\" style=\"text-align: justify;\">\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">t<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">3<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">4<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">6<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">7<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">8<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">9<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">11<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5t<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(c) Complete the table and find the solution of the equation <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{z}{3}\" alt=\"\\frac{z}{3}\" align=\"absmiddle\" \/> = 4 using the table.<\/strong><\/span><\/p>\n<div class=\"table-responsive\" style=\"text-align: justify;\">\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">z<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">8<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">9<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">11<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">12<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">13<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">14<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">15<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">16<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{z}{3}\" alt=\"\\frac{z}{3}\" align=\"absmiddle\" \/><\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\frac{2}{3}\" alt=\"2\\frac{2}{3}\" align=\"absmiddle\" \/><\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">3<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?3\\frac{1}{3}\" alt=\"3\\frac{1}{3}\" align=\"absmiddle\" \/><\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(d) Complete the table and find the solution to the equation m \u2013 7 = 3.<\/strong><\/span><\/p>\n<div class=\"table-responsive\" style=\"text-align: justify;\">\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">m<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">6<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">7<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">8<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">9<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">11<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">12<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">13<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">m \u2013 7<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2014<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solutions:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(a)\u00a0<\/strong>For m + 10, the table is represented as below<\/span><\/p>\n<div class=\"table-responsive\" style=\"text-align: justify;\">\n<table class=\"table table-bordered\" style=\"width: 40%;\">\n<tbody>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">m<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">m + 10<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">1<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">1 + 10 = 11<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">2<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">2 + 10 = 12<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">3<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">3 + 10 = 13<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">4<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">4 + 10 = 14<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5 + 10 = 15<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">6<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">6 + 10 = 16<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">7<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">7 + 10 = 17<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">8<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">8 + 10 = 18<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">9<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">9 + 10 = 19<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10 = 10 = 20<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Now, by inspection we may conclude that m = 6 is the solution of the above equation since, for m = 6,<br \/>\nm + 10 = 6 + 10 = 16<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(b)<\/strong> For 5t, the table is represented as below<\/span><\/p>\n<div class=\"table-responsive\" style=\"text-align: justify;\">\n<table class=\"table table-bordered\" style=\"width: 40%;\">\n<tbody>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">t<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5t<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">3<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5 \u00d7 3 = 15<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">4<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5 \u00d7 4 = 20<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5 \u00d7 5 = 25<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">6<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5 \u00d7 6 = 30<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">7<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5 \u00d7 7 = 35<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">8<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5 \u00d7 8 = 40<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">9<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5 \u00d7 9 = 45<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5 \u00d7 10 = 50<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">11<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5 \u00d7 11 = 55<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Now, by inspection we may conclude that t = 7 is the solution of the above equation since, for t = 7,<br \/>\n5t = 5 \u00d7 7 = 35<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(c)<\/strong> For <strong><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{z}{3}\" alt=\"\\frac{z}{3}\" align=\"absmiddle\" \/><\/strong>, the table is represented as below<\/span><\/p>\n<div class=\"table-responsive\" style=\"text-align: justify;\">\n<table class=\"table table-bordered\" style=\"width: 40%;\" width=\"40%\">\n<tbody>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">z<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{z}{3}\" alt=\"\\frac{z}{3}\" align=\"absmiddle\" \/><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">8<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{3}\" alt=\"\\frac{8}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\frac{2}{3}\" alt=\"2\\frac{2}{3}\" align=\"absmiddle\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">9<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{3}\" alt=\"\\frac{9}{3}\" align=\"absmiddle\" \/> = 3<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{10}3{}\" alt=\"\\frac{10}3{}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?3\\frac{1}{3}\" alt=\"3\\frac{1}{3}\" align=\"absmiddle\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">11<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{11}{3}\" alt=\"\\frac{11}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?3\\frac{2}{3}\" alt=\"3\\frac{2}{3}\" align=\"absmiddle\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">12<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{12}{3}\" alt=\"\\frac{12}{3}\" align=\"absmiddle\" \/> = 4<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">13<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{13}{3}\" alt=\"\\frac{13}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?4\\frac{1}{3}\" alt=\"4\\frac{1}{3}\" align=\"absmiddle\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">14<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{14}{3}\" alt=\"\\frac{14}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?4\\frac{2}{3}\" alt=\"4\\frac{2}{3}\" align=\"absmiddle\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">15<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{3}\" alt=\"\\frac{15}{3}\" align=\"absmiddle\" \/> = 5<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">16<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{16}{3}\" alt=\"\\frac{16}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?5\\frac{1}{3}\" alt=\"5\\frac{1}{3}\" align=\"absmiddle\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Now, by inspection we may conclude that z = 12 is the solution of the above equation since for z = 12,<\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{z}{3}\" alt=\"\\frac{z}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{12}{3}\" alt=\"\\frac{12}{3}\" align=\"absmiddle\" \/> = 4<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(d)<\/strong> For m \u2013 7, the table is represented as below<\/span><\/p>\n<div class=\"table-responsive\" style=\"text-align: justify;\">\n<table class=\"table table-bordered\" style=\"width: 40%;\">\n<tbody>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">m<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">m \u2013 7<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">5 \u2013 7 = -2<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">6<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">6 \u2013 7 = -1<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">7<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">7 \u2013 7 = 0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">8<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">8 \u2013 7 = 1<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">9<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">9 \u2013 7 = 2<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">10 \u2013 7 = 3<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">11<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">11 \u2013 7 = 4<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">12<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">12 \u2013 7 = 5<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">13<\/span><\/td>\n<td><span style=\"color: #000000; font-family: georgia, palatino, serif;\">13 \u2013 7 = 6<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Now, by inspection we may conclude that m = 10 is the solution of the above equation since, for m = 10,<br \/>\nm \u2013 7 = 10 \u2013 7 = 3<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>5. Solve the following riddles, you may yourself construct such riddles.<\/strong><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Who am I?<\/strong><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-584 alignright\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-11.5Q5.png\" alt=\"NCERT Class 6 Math Solution\" width=\"322\" height=\"434\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-11.5Q5.png 364w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-11.5Q5-222x300.png 222w\" sizes=\"auto, (max-width: 322px) 100vw, 322px\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(i) Go round a square<br \/>\nCounting every corner<br \/>\nThrice and no more!<br \/>\nAdd the count to me<br \/>\nTo get exactly thirty four!<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(ii) For each day of the week<br \/>\nMake an upcount from me<br \/>\nIf you make no mistake<br \/>\nYou will get twenty three!<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(iii) I am a special number<br \/>\nTake away from me a six!<br \/>\nA whole cricket team<br \/>\nYou will still be able to fix!<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(iv) Tell me who I am<br \/>\nI shall give a pretty clue!<br \/>\nYou will get me back<br \/>\nIf you take me out of twenty two!<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solutions:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i)\u00a0<\/strong>There are 4 corners in a square.<br \/>\nThrice the number of corners in the square = 3 \u00d7 4 = 12<br \/>\nWhen 12 is added to the number it becomes 34<br \/>\nSo, the number will be the difference of 34 and 12<br \/>\n34 \u2013 12 = 22<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(ii) The result was 23 when the old number was up counted on Sunday<br \/>\nThe result was 22 when the old number was up counted on Saturday<br \/>\nThe result was 21 when the old number was up counted on Friday<br \/>\nThe result was 20 when the old number was up counted on Thursday<br \/>\nThe result was 19 when the old number was up counted on Wednesday<br \/>\nThe result was 18 when the old number was up counted on Tuesday<br \/>\nThe result was 17 when the old number was up counted on Monday<br \/>\nHence, the number taken at starting was 17 \u2013 1 = 16<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(iii) There are 11 players in a cricket team<br \/>\nIf 6 is subtracted from a required number it will be 11<br \/>\n11 + 6 = 17<br \/>\nHence, the number is 17<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(iv) The required number is such that if it is subtracted from 22 the result is the number itself.<br \/>\nThe number is 11 because if it is subtracted from 22 the result will be 11 only.<\/span><\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 100%; background-color: #f2e079; text-align: center;\"><span style=\"color: #000000; font-size: 14pt; font-family: georgia, palatino, serif;\"><strong>NCERT Class 6<sup>th\u00a0<\/sup>Solution\u00a0<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%; text-align: left;\"><span style=\"color: #ff0000; font-size: 14pt; font-family: georgia, palatino, serif;\"><strong><span style=\"color: #0000ff; font-size: 12pt;\"><a class=\"row-title\" style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-english\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 English\u201d (Edit)\">NCERT Solutions Class 6 English<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%; text-align: left;\"><span style=\"color: #ff0000; font-size: 14pt; font-family: georgia, palatino, serif;\"><strong><span style=\"color: #0000ff; font-size: 12pt;\"><a class=\"row-title\" style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-hindi\/\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 6 Hindi<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%; text-align: left;\"><span style=\"color: #ff0000; font-size: 14pt; font-family: georgia, palatino, serif;\"><strong><span style=\"color: #0000ff; font-size: 12pt;\"><a class=\"row-title\" style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 6 Maths<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%; text-align: left;\"><span style=\"font-family: georgia, palatino, serif;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-sanskrit\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000; font-size: 14pt;\"><strong><span style=\"color: #0000ff; font-size: 12pt;\">NCERT Solutions Class 6 Sanskrit<\/span><\/strong><\/span><\/a><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%; text-align: left;\"><span style=\"color: #ff0000; font-size: 14pt; font-family: georgia, palatino, serif;\"><strong><span style=\"color: #0000ff; font-size: 12pt;\"><a class=\"row-title\" style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 6 Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%; text-align: left;\"><span style=\"color: #ff0000; font-size: 14pt; font-family: georgia, palatino, serif;\"><strong><span style=\"color: #0000ff; font-size: 12pt;\"><a class=\"row-title\" style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-social-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 6 Social Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 6 Maths Chapter &#8211; 11 (Algebra) The NCERT Solutions in English Language for Class 6 Mathematics Chapter &#8211; 11 Algebra Exercise 11.5 has been provided here to help the students in solving the questions from this exercise. Chapter 11: Algebra NCERT Solution Class 6 Maths Exercise &#8211; 11.1 NCERT Solution Class 6 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[25,26,4,5],"class_list":["post-562","post","type-post","status-publish","format-standard","hentry","category-class-6-maths","tag-chapter-11-algebra-in-english","tag-ncert-solutions-class-6-maths-chapter-11-in-english","tag-ncert-solutions-class-6-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.5) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 6 Maths Chapter 11 Algebra Ex 11.5 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"The NCERT Solutions in English Language for Class 6 Mathematics Chapter - 11 Algebra Exercise 11.5 has been provided here to help the students in solving the questions from this exercise.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-11-algebra-ex-11-5\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions Class 6 Maths Chapter 11 Algebra Ex 11.5\" \/>\n<meta property=\"og:description\" content=\"The NCERT Solutions in English Language for Class 6 Mathematics Chapter - 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