Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 7 - Algebraic Fractions - Chapters 1-7 Cumulative Review Problem Set - Page 324: 55



Work Step by Step

We use the distributive property in order to put the equation into trinomial form. We then use the rules of factoring trinomials and set the equation equal to zero to solve the equation: $(x+1)(x+6)=24$ $x(x+6)+1(x+6)=24$ $x^{2}+6x+x+6=24$ $x^{2}+7x+6-24=0$ $x^{2}+7x-18=0$ $x^{2}-2x+9x-18=0$ $x(x-2)+9(x-2)=0$ $(x-2)(x+9)=0$ $(x-2)=0$ or $(x+9)=0$ $x=2$ or $x=-9$ Therefore, the solution set is {$2,-9$}.
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