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: 7

Answer

$x=\{ -5,5 \}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $ |4x|=20 ,$ is equivalent to \begin{array}{l}\require{cancel} 4x=20 \text{ OR } 4x=-20 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 4x=20 \\\\ x=\dfrac{20}{4} \\\\ x=5 \\\\\text{ OR }\\\\ 4x=-20 \\\\ x=-\dfrac{20}{4} \\\\ x=-5 .\end{array} Hence, the solutions are $ x=\{ -5,5 \} .$
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