Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 9 - Inequalities and Problem Solving - 9.3 Absolute-Value Equations and Inequalities - 9.3 Exercise Set: 110

Answer

$|x+2|\lt3$

Work Step by Step

Adding $2$ to all sides of the given inequality $ -5\lt x \lt 1 ,$ then the given is equivalent to \begin{array}{l}\require{cancel} -5+2\lt x+2 \lt 1+2 \\\\ -3\lt x+2 \lt 3 .\end{array} 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 $ |x+2|\lt3 .$
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