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: 22

Answer

$x\gt-\dfrac{2}{17}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ 2(4+2x)\gt2x+3(2-5x) ,$ 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} 2(4+2x)\gt2x+3(2-5x) \\\\ 2(4)+2(2x)\gt2x+3(2)+3(-5x) \\\\ 8+4x\gt2x+6-15x .\end{array} Using the properties of inequality to isolate the variable, then \begin{array}{l}\require{cancel} 8+4x\gt2x+6-15x \\\\ 4x-2x+15x\gt6-8 \\\\ 17x\gt-2 \\\\ x\gt-\dfrac{2}{17} .\end{array}
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