Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 2 - Section 2.5 - Compound Inequalities - Exercise Set - Page 94: 29


$\text{ the interval } \left[ -3,\dfrac{3}{2} \right] $

Work Step by Step

Using properties of inequality, then, \begin{array}{l} 1\le \dfrac{2}{3}x+3\le4\\\\ 1-3\le \dfrac{2}{3}x+3-3\le4-3\\\\ -2\le \dfrac{2}{3}x\le1\\\\ -2\cdot\dfrac{3}{2}\le \dfrac{3}{2}\cdot\dfrac{2}{3}x\le1\cdot\dfrac{3}{2}\\\\ -3\le x\le\dfrac{3}{2} .\end{array} Hence, the solution set is $ \text{ the interval } \left[ -3,\dfrac{3}{2} \right] $.
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