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: 21

Answer

$t\lt\dfrac{29}{5}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ 5(t-3)+4t\lt2(7+2t) ,$ use the Distributive Property and the properties of inequality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to \begin{array}{l}\require{cancel} 5(t-3)+4t\lt2(7+2t) \\\\ 5(t)+5(-3)+4t\lt2(7)+2(2t) \\\\ 5t-15+4t\lt14+4t .\end{array} Using the properties of inequality to isolate the variable, then \begin{array}{l}\require{cancel} 5t-15+4t\lt14+4t \\\\ 5t+4t-4t\lt14+15 \\\\ 5t\lt29 \\\\ t\lt\dfrac{29}{5} .\end{array}
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