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 - 9.3 Absolute-Value Equations and Inequalities - 9.3 Exercise Set: 52

Answer

$t=\left\{ -4,-\dfrac{10}{9} \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |5t+7|=|4t+3| ,$ use the definition of absolute value equality. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Since $|x|=|y|$ implies $x=y \text{ or } x=-y,$ the equation above is equivalent to \begin{array}{l}\require{cancel} 5t+7=4t+3 \\\\\text{OR}\\\\ 5t+7=-(4t+3) .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 5t+7=4t+3 \\\\ 5t-4t=3-7 \\\\ t=-4 \\\\\text{OR}\\\\ 5t+7=-(4t+3) \\\\ 5t+7=-4t-3 \\\\ 5t+4t=-3-7 \\\\ 9t=-10 \\\\ t=-\dfrac{10}{9} .\end{array} Hence, $ t=\left\{ -4,-\dfrac{10}{9} \right\} .$
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