College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Review Exercises - Page 166: 111


$x=\{ -11,3 \}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the given inequality, $ |x+4|=7 ,$ is equivalent to \begin{array}{l}\require{cancel} x+4=7 \\\text{ OR }\\ x+4=-7 .\end{array} Solving each equation separately, then, \begin{array}{l}\require{cancel} x=7-4 \\\\ x=3 \\\text{ OR }\\ x+4=-7 \\\\ x=-7-4 \\\\ x=-11 .\end{array} Hence, $ x=\{ -11,3 \} .$
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