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 - 9.1 Inequalities and Applications - 9.1 Exercise Set: 18

Answer

$t\le-6$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ \dfrac{2t-9}{-3}\ge7 .$ $\bf{\text{Solution Details:}}$ Multiplying both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to \begin{array}{l}\require{cancel} \dfrac{2t-9}{-3}\ge7 \\\\ -3\left( \dfrac{2t-9}{-3} \right)\ge-3(7) \\\\ 2t-9\le-21 .\end{array} Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} 2t-9\le-21 \\\\ 2t\le-21+9 \\\\ 2t\le-12 \\\\ t\le-\dfrac{12}{2} \\\\ t\le-6 .\end{array}
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