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: 48


$x=\left\{ -4,1 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |3x+2|=|x-6| ,$ use the definition of an absolute 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} 3x+2=x-6 \\\\\text{OR}\\\\ 3x+2=-(x-6) .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 3x+2=x-6 \\\\ 3x-x=-6-2 \\\\ 2x=-8 \\\\ x=-\dfrac{8}{2} \\\\ x=-4 \\\\\text{OR}\\\\ 3x+2=-(x-6) \\\\ 3x+2=-x+6 \\\\ 3x+x=6-2 \\\\ 4x=4 \\\\ x=\dfrac{4}{4} \\\\ x=1 .\end{array} Hence, $ x=\left\{ -4,1 \right\} .$
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