Intermediate Algebra (6th Edition)

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

Chapter 2 - Section 2.4 - Linear Inequalities and Problem Solving - Exercise Set - Page 85: 42

Answer

$\left( \infty,\dfrac{1}{2} \right]$

Work Step by Step

Using the properties of inequality, the expression $ \dfrac{3}{4}-\dfrac{2}{3}\ge\dfrac{x}{6} $ simplifies to \begin{array}{l} 12\left( \dfrac{3}{4}-\dfrac{2}{3} \right)\ge \left( \dfrac{x}{6} \right) 12 \\\\ 3(3)-4(2)\ge 2x \\ 9-8\ge 2x \\ 1\ge 2x \\ \dfrac{1}{2}\ge x \\ x\le \dfrac{1}{2} .\end{array} In interval notation, the solution set is $ \left( \infty,\dfrac{1}{2} \right] $.
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