Intermediate Algebra (12th Edition)

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

Chapter 5 - Chapters R-5 - Cumulative Review Exercises: 11

Answer

$(-11,7)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ |x+2|\lt9 ,$ use the definition of the absolute value less than a constant. $\bf{\text{Solution Details:}}$ Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ or $|x|\le c$ implies $-c\le x\le c$ the inequality above is equivalent to \begin{array}{l}\require{cancel} -9\lt x+2\lt9 .\end{array} Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -9-2\lt x+2-2\lt9-2 \\\\ -11\lt x\lt7 .\end{array} Hence, the solution set is the interval $ (-11,7) .$
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