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: 9


$x=\{ -6,12 \}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $ |x-3|=9 ,$ is equivalent to \begin{array}{l}\require{cancel} x-3=9 \text{ OR } x-3=-9 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} x-3=9 \\\\ x=9+3 \\\\ x=12 \\\\\text{ OR }\\\\ x-3=-9 \\\\ x=-9+3 \\\\ x=-6 .\end{array} Hence, the solutions are $ x=\{ -6,12 \} .$
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