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: 17

Answer

$t\ge-\dfrac{13}{3}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ \dfrac{3t-7}{-4}\le5 .$ $\bf{\text{Solution Details:}}$ 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{3t-7}{-4}\le5 \\\\ -4\left( \dfrac{3t-7}{-4} \right)\le-4(5) \\\\ 3t-7\ge-20 .\end{array} Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} 3t-7\ge-20 \\\\ 3t\ge-20+7 \\\\ 3t\ge-13 \\\\ t\ge-\dfrac{13}{3} .\end{array}
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