Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 9 - Inequalities and Problem Solving - 9.3 Absolute-Value Equations and Inequalities - 9.3 Exercise Set - Page 599: 55



Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |7-4a|=|4a+5| ,$ use the definition of an absolute value equality. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Since $|x|=|y|$ implies $x=y \text{ or } x=-y,$ the equation above is equivalent to \begin{array}{l}\require{cancel} 7-4a=4a+5 \\\\\text{OR}\\\\ 7-4a=-(4a+5) .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 7-4a=4a+5 \\\\ -4a-4a=5-7 \\\\ -8a=-2 \\\\ a=\dfrac{-2}{-8} \\\\ a=\dfrac{1}{4} \\\\\text{OR}\\\\ 7-4a=-(4a+5) \\\\ 7-4a=-4a-5 \\\\ -4a+4a=-5-7 \\\\ 0=-12 \text{ (FALSE)} .\end{array} Hence, $ a=\dfrac{1}{4} .$
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