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: 47

Answer

$x=\left\{ -8,2 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |x-7|=|2x+1| ,$ 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} x-7=2x+1 \\\\\text{OR}\\\\ x-7=-(2x+1) .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} x-7=2x+1 \\\\ x-2x=1+7 \\\\ -x=8 \\\\ x=-8 \\\\\text{OR}\\\\x-7=-(2x+1) \\\\ x-7=-2x-1 \\\\ x+2x=-1+7 \\\\ 3x=6 \\\\ x=\dfrac{6}{3} \\\\ x=2 .\end{array} Hence, $ x=\left\{ -8,2 \right\} .$
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