Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 1 - Review Exercises: 62


$x=\{ 7,-11 \}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the given equation, $ |x+2|=9 ,$ is equivalent to \begin{array}{l}\require{cancel} x+2=9 \text{ OR } x+2=-9 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} x+2=9 \\\\ x=9-2 \\\\ x=7 \\\\\text{ OR }\\\\ x+2=-9 \\\\ x=-9-2 \\\\ x=-11 .\end{array} Hence, the solutions are $ x=\{ 7,-11 \} .$
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