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: 21

Answer

$x=\left\{ -\dfrac{1}{2},\dfrac{7}{2} \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |2x-3|=4 ,$ 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} 2x-3=4 \\\\\text{OR}\\\\ 2x-3=-4 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 2x-3=4 \\\\ 2x=4+3 \\\\ 2x=7 \\\\ x=\dfrac{7}{2} \\\\\text{OR}\\\\ 2x-3=-4 \\\\ 2x=-4+3 \\\\ 2x=-1 \\\\ x=-\dfrac{1}{2} .\end{array} Hence, $ x=\left\{ -\dfrac{1}{2},\dfrac{7}{2} \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.