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: 31


$x=\left\{ -8,8 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |5x|-3=37 ,$ isolate first the absolute value expression. Then use the definition of an absolute value equality. $\bf{\text{Solution Details:}}$ Using the properties of equality, the given equation is equivalent to \begin{array}{l}\require{cancel} |5x|-3=37 \\\\ |5x|=37+3 \\\\ |5x|=40 .\end{array} Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the given equation is equivalent to \begin{array}{l}\require{cancel} 5x=40 \\\\\text{OR}\\\\ 5x=-40 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 5x=40 \\\\ x=\dfrac{40}{5} \\\\ x=8 \\\\\text{OR}\\\\ 5x=-40 \\\\ x=-\dfrac{40}{5} \\\\ x=-8 .\end{array} Hence, $ x=\left\{ -8,8 \right\} .$
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