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 - Test: Chapter 9: 3

Answer

$x\le\dfrac{9}{16}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Distributive Property and the properties of inequality to solve the given, $ -2(3x-1)-5\ge6x-4(3-x) .$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} -2(3x-1)-5\ge6x-4(3-x) \\\\ -2(3x)-2(-1)-5\ge6x-4(3)-4(-x) \\\\ -6x+2-5\ge6x-12+4x .\end{array} Using the properties of equality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -6x+2-5\ge6x-12+4x \\\\ -6x-6x-4x\ge-12-2+5 \\\\ -16x\ge-9 .\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} -16x\ge-9 \\\\ x\le\dfrac{-9}{-16} \\\\ x\le\dfrac{9}{16} .\end{array}
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