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 - Review Exercises: Chapter 9 - Page 623: 35


$x=\left\{ -14,\dfrac{4}{3} \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |2x+5|=|x-9| ,$ use the definition of 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} 2x+5=x-9 \\\\\text{OR}\\\\ 2x+5=-(x-9) .\end{array} Using the properties of equality to isolate the variable in each equation results to \begin{array}{l}\require{cancel} 2x+5=x-9 \\\\ 2x-x=-9-5 \\\\ x=-14 \\\\\text{OR}\\\\ 2x+5=-(x-9) \\\\ 2x+5=-x+9 \\\\ 2x+x=9-5 \\\\ 3x=4 \\\\ x=\dfrac{4}{3} .\end{array} Hence, $ x=\left\{ -14,\dfrac{4}{3} \right\} .$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.