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: 41

Answer

$\left( \infty,7 \right]$

Work Step by Step

Using the properties of inequality, the expression $ \dfrac{1}{2}+\dfrac{2}{3}\ge\dfrac{x}{6} $ simplifies to \begin{array}{l} 6\left( \dfrac{1}{2}+\dfrac{2}{3}\right)\ge \left( \dfrac{x}{6} \right) 6 \\\\ 3(1)+2(2)\ge x \\ 3+4\ge x \\ 7\ge x \\ x\le 7 .\end{array} In interval notation, the solution set is $ \left( \infty,7 \right] $.
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