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 - Review Exercises: Chapter 2 - Page 149: 2


$NOT \ equivalent$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ 5-2t\lt9 .$ If the solution set of this is the same as the second inequality, $ t\gt6 ,$ then the inequalities are equivalent. $\bf{\text{Solution Details:}}$ Using the properties of inequality to isolate the variable, then \begin{array}{l}\require{cancel} 5-2t\lt9 \\\\ -2t\lt9-5 \\\\ -2t\lt4 .\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} -2t\lt4 \\\\ t\gt\dfrac{4}{-2} \\\\ t\gt-2 .\end{array} Since the solution set of $t\gt-2$ is not the same as the solution set of the other given inequality, $t\gt6,$ then the two inequalities are $\text{ NOT equivalent .}$
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