Intermediate Algebra (6th Edition)

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

Chapter 2 - Test - Page 114: 16

Answer

$\text{the interval } \left( \dfrac{3}{2},5 \right] $

Work Step by Step

Using the properties of inequalities, the solution to the given inequality, $ -3 \lt 2(x-3) \le 4 ,$ is \begin{array}{l}\require{cancel} -3 \lt 2x-6 \le 4 \\\\ -3+6 \lt 2x-6+6 \le 4+6 \\\\ 3 \lt 2x \le 10 \\\\ \dfrac{3}{2} \lt \dfrac{2}{2}x \le \dfrac{10}{2} \\\\ \dfrac{3}{2} \lt x \le 5 .\end{array} In interval notation, the solution is $ \text{the interval } \left( \dfrac{3}{2},5 \right] .$
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