Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.8 - Inequalities - 1.8 Exercises - Page 89: 79


$\left[ 2,8 \right] $

Work Step by Step

For any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a$. (The symbol $\lt$ may be replaced with $\le$.) Using the concept above, the solutions to the given inequality, $ |x-5|\le3 ,$ is \begin{array}{l}\require{cancel} -3\le x-5\le3 \\\\ -3+5\le x\le3+5 \\\\ 2\le x\le8 .\end{array} In interval notation, the solution set is $ \left[ 2,8 \right] .$
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