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: 12

Answer

NOT equivalent

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequalities, \begin{array}{l}\require{cancel} -2t+3\ge11 \\\text{and}\\ -2t\ge14 .\end{array} If the solutions are the same, then the given inequalities are equivalent. $\bf{\text{Solution Details:}}$ Using the properties of inequality, the solution of the first inequality is \begin{array}{l}\require{cancel} -2t+3\ge11 \\\\ -2t\ge11-3 \\\\ -2t\ge8 \\\\ t\le\dfrac{8}{-2} \\\\ t\le-4 .\end{array} Using the properties of inequality, the solution of the second inequality is \begin{array}{l}\require{cancel} -2t\ge14 \\\\ t\le\dfrac{14}{-2} \\\\ t\le-7 .\end{array} Since the solutions of both inequalities are NOT the same, then the given inequalities are $\text{ NOT equivalent .}$
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