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: 27


$\left[ -\dfrac{9}{2},\dfrac{15}{2} \right]$

Work Step by Step

Using the properties of inequality, the given inequality, $ -6\le\dfrac{3}{2}-x\le6 ,$ simplifies to \begin{array}{l}\require{cancel} 2(-6)\le2\left( \dfrac{3}{2}-x \right)\le2(6) \\\\ -12\le3-2x\le12 \\\\ -12-3\le3-3-2x\le12-3 \\\\ -15\le-2x\le9 \\\\ \dfrac{-15}{-2}\ge\dfrac{-2x}{-2}\ge\dfrac{9}{-2} \\\\ \dfrac{15}{2}\ge x\ge-\dfrac{9}{2} \\\\ -\dfrac{9}{2}\le x\le\dfrac{15}{2} .\end{array} Hence, the solution is $ \left[ -\dfrac{9}{2},\dfrac{15}{2} \right] .$
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