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: 22


$x=\left\{ -30,30 \right\}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $ |0.3x|=9 ,$ is equivalent to \begin{array}{l}\require{cancel} 0.3x=9 \text{ OR } 0.3x=-9 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 0.3x=9 \\\\ 10(0.3x)=(9)10 \\\\ 3x=90 \\\\ x=\dfrac{90}{3} \\\\ x=30 \\\\\text{ OR }\\\\ 0.3x=-9 \\\\ 10(0.3x)=(-9)10 \\\\ 3x=-90 \\\\ x=-\dfrac{90}{3} \\\\ x=-30 .\end{array} Hence, the solutions are $ x=\left\{ -30,30 \right\} .$
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