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: 80

Answer

$x=\left\{ -7,7 \right\}$

Work Step by Step

Using the properties of equality, the given equation, $ |x|+3=10 ,$ is equivalent to \begin{array}{l}\require{cancel} |x|=10-3 \\\\ |x|=7 .\end{array} Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the equation above is equivalent to \begin{array}{l}\require{cancel} x=7 \text{ OR }x=-7 .\end{array} Hence, the solutions are $ x=\left\{ -7,7 \right\} .$
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