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: 111

Answer

$x\le-4a$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the order of operations and the properties of inequality to solve the given inequality, $ -(x+5)\ge4a-5 .$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to \begin{array}{l}\require{cancel} -(x+5)\ge4a-5 \\\\ -1(x)-1(5)\ge4a-5 \\\\ -x-5\ge4a-5 .\end{array} Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} -x-5\ge4a-5 \\\\ -x\ge4a-5+5 \\\\ -x\ge4a .\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} -x\ge4a \\\\ \dfrac{-x}{-1}\ge\dfrac{4a}{-1} \\\\ x\le-4a .\end{array}
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