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 - Page 118: 10


$x=\{ -8,18 \}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $ |x-5|=13 ,$ is equivalent to \begin{array}{l}\require{cancel} x-5=13 \text{ OR } x-5=-13 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} x-5=13 \\\\ x=13+5 \\\\ x=18 \\\\\text{ OR }\\\\ x-5=-13 \\\\ x=-13+5 \\\\ x=-8 .\end{array} Hence, the solutions are $ x=\{ -8,18 \} .$
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