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: 22

Answer

$x=\left\{ -\dfrac{9}{5},1 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |5x+2|=7 ,$ use the definition of an absolute value equality. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ 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+2=7 \\\\\text{OR}\\\\ 5x+2=-7 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 5x+2=7 \\\\ 5x=7-2 \\\\ 5x=5 \\\\ x=\dfrac{5}{5} \\\\ x=1 \\\\\text{OR}\\\\ 5x+2=-7 \\\\ 5x=-7-2 \\\\ 5x=-9 \\\\ x=-\dfrac{9}{5} .\end{array} Hence, $ x=\left\{ -\dfrac{9}{5},1 \right\} .$
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