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 - Review Exercises: Chapter 9: 9

Answer

$x\le-\dfrac{5}{2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Distributive Property and the properties of inequality to solve the given, $ -2(x-5)\ge6(x+7)-12 .$ $\bf{\text{Solution Details:}}$ 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(x-5)\ge6(x+7)-12 \\\\ -2(x)-2(-5)\ge6(x)+6(7)-12 \\\\ -2x+10\ge6x+42-12 .\end{array} Using the properties of equality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -2x+10\ge6x+42-12 \\\\ -2x-6x\ge42-12-10 \\\\ -8x\ge20 .\end{array} Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to \begin{array}{l}\require{cancel} -8x\ge20 \\\\ x\le\dfrac{20}{-8} \\\\ x\le-\dfrac{5}{2} .\end{array}
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