Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 1 - Section 1.7 - Absolute Value Equations and Inequalities - 1.7 Exercises: 15

Answer

$x=\left\{ -\dfrac{19}{2},\dfrac{9}{2} \right\}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $ |2x+5|=14 ,$ is equivalent to \begin{array}{l}\require{cancel} 2x+5=14 \text{ OR } 2x+5=-14 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 2x+5=14 \\\\ 2x=14-5 \\\\ 2x=9 \\\\ x=\dfrac{9}{2} \\\\\text{ OR }\\\\ 2x+5=-14 \\\\ 2x=-14-5 \\\\ 2x=-19 \\\\ x=-\dfrac{19}{2} .\end{array} Hence, the solutions are $ x=\left\{ -\dfrac{19}{2},\dfrac{9}{2} \right\} .$
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