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: 2

Answer

$x\gt\dfrac{16}{5}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Distributive Property and the properties of inequality to solve the given, $ 3(7-x)\lt2x+5 .$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 3(7-x)\lt2x+5 \\\\ 3(7)+3(-x)\lt2x+5 \\\\ 21-3x\lt2x+5 .\end{array} Using the properties of equality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 21-3x\lt2x+5 \\\\ -3x-2x\lt5-21 \\\\ -5x\lt-16 .\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} -5x\lt-16 \\\\ x\gt\dfrac{-16}{-5} \\\\ x\gt\dfrac{16}{5} .\end{array}
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