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 9 - Inequalities and Problem Solving - 9.1 Inequalities and Applications - 9.1 Exercise Set: 23

Answer

$m\gt\dfrac{7}{3}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ 5[3m-(m+4)]\gt-2(m-4) ,$ use the Distributive Property and the properties of inequality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to \begin{array}{l}\require{cancel} 5[3m-(m+4)]\gt-2(m-4) \\\\ 5[3m-1(m)-1(4)]\gt-2(m)-2(-4) \\\\ 5[3m-m-4]\gt-2m+8 \\\\ 5[3m]+5[-m]+5[-4]\gt-2m+8 \\\\ 15m-5m-20\gt-2m+8 .\end{array} Using the properties of inequality to isolate the variable, then \begin{array}{l}\require{cancel} 15m-5m-20\gt-2m+8 \\\\ 15m-5m+2m\gt8+20 \\\\ 12m\gt28 \\\\ m\gt\dfrac{28}{12} \\\\ m\gt\dfrac{7}{3} .\end{array}
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