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: 97

Answer

$x\gt-\dfrac{5}{32}$

Work Step by Step

Using the Distributive Property and the properties of inequality, the solution to the given inequality, $ \dfrac{2}{3}\left(\dfrac{7}{8}-4x\right)-\dfrac{5}{8}\lt\dfrac{3}{8} ,$ is \begin{array}{l}\require{cancel} \dfrac{2}{3}\left(\dfrac{7}{8}\right)+\dfrac{2}{3}(-4x)-\dfrac{5}{8}\lt\dfrac{3}{8} \\\\ \dfrac{14}{24}-\dfrac{8}{3}x-\dfrac{5}{8}\lt\dfrac{3}{8} \\\\ 24\left( \dfrac{14}{24}-\dfrac{8}{3}x-\dfrac{5}{8}\right)\lt\left(\dfrac{3}{8}\right)24 \\\\ 1(14)+8(-8x)+3(-5)\lt3(3) \\\\ 14-64x-15\lt9 \\\\ -64x\lt9-14+15 \\\\ -64x\lt10 \\\\ x\gt\dfrac{10}{-64} \\\\ x\gt\dfrac{\cancel{2}\cdot5}{\cancel{2}\cdot(-32)} \\\\ x\gt\dfrac{5}{-32} \\\\ x\gt-\dfrac{5}{32} .\end{array}
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