Intermediate Algebra (12th Edition)

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

Chapter 1 - Mixed Review Exercises - Page 132: 11


$\left( -3,\dfrac{7}{2} \right)$

Work Step by Step

Using the properties of inequality, the given inequality, $ -4\lt3-2x\lt9 ,$ simplifies to \begin{array}{l}\require{cancel} -4-3\lt3-3-2x\lt9-3 \\\\ -7\lt -2x\lt6 \\\\ \dfrac{-7}{-2}\gt \dfrac{-2x}{-2}\gt\dfrac{6}{-2} \\\\ \dfrac{7}{2}\gt x\gt-3 \\\\ -3\lt x\lt\dfrac{7}{2} .\end{array} Hence, the solution is the interval $ \left( -3,\dfrac{7}{2} \right) .$
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