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 86: 60

Answer

$\left( -\infty, -\dfrac{12}{5} \right]$

Work Step by Step

Using the properties of inequality, the expression $ \dfrac{7}{12}x-\dfrac{1}{3}\le\dfrac{3}{8}x-\dfrac{5}{6} $ simplifies to \begin{array}{l} 24\left( \dfrac{7}{12}x-\dfrac{1}{3} \right)\le\left( \dfrac{3}{8}x-\dfrac{5}{6} \right)24\\\\ 2(7x)-8(1)\le3(3x)-4(5)\\ 14x-8\le9x-20\\ 14x-9x\le-20+8\\ 5x\le-12\\ x\le-\dfrac{12}{5} .\end{array} In interval notation, the solution set is $ \left( -\infty, -\dfrac{12}{5} \right] $.
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