Intermediate Algebra (12th Edition)

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

Chapter 1 - Summary Exercises - Reviewing a Chapter - Solving Linear and Absolute Value Equations and Inequalities - Page 122: 31


$\left[ -\dfrac{1}{3}, 3 \right]$

Work Step by Step

Using the properties of inequality, the given inequality, $ -2\le 3x-1\le 8 ,$ simplifies to \begin{array}{l}\require{cancel} -2+1\le 3x-1+1\le 8+1 \\\\ -1\le 3x\le 9 \\\\ -\dfrac{1}{3}\le x\le \dfrac{9}{3} \\\\ -\dfrac{1}{3}\le x\le 3 .\end{array} Hence, the solution is the interval $ \left[ -\dfrac{1}{3}, 3 \right] .$
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