Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 2 - Equations, Inequalities, and Problem Solving - 2.6 Solving Inequalities - 2.6 Exercise Set: 98

Answer

$x\lt\dfrac{11}{18}$

Work Step by Step

Using the Distributive Property and the properties of inequality, the solution to the given inequality, $ \dfrac{3}{4}\left(3x-\dfrac{1}{2}\right)-\dfrac{2}{3}\lt\dfrac{1}{3} ,$ is \begin{array}{l}\require{cancel} \dfrac{9x}{4}-\dfrac{3}{8}-\dfrac{2}{3}\lt\dfrac{1}{3} \\\\ 24\left( \dfrac{9x}{4}-\dfrac{3}{8}-\dfrac{2}{3} \right) \lt\left( \dfrac{1}{3} \right)24 \\\\ 6(9x)+3(-3)+8(-2)\lt1(8) \\\\ 54x-9-16\lt8 \\\\ 54x\lt8+9+16 \\\\ 54x\lt33 \\\\ x\lt\dfrac{33}{54} \\\\ x\lt\dfrac{\cancel{3}\cdot11}{\cancel{3}\cdot18} \\\\ x\lt\dfrac{11}{18} .\end{array}
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