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 - Page 599: 38


$t=\left\{ 4,10 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |t-7|+1=4 ,$ isolate first the absolute value expression. Then use the definition of an absolute value equality. Finally, use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the proeprties of equality to isolate the absolute value expression, the given is equivalent to \begin{array}{l}\require{cancel} |t-7|+1=4 \\\\ |t-7|=4-1 \\\\ |t-7|=3 .\end{array} Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the given equation is equivalent to \begin{array}{l}\require{cancel} t-7=3 \\\\\text{OR}\\\\ t-7=-3 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} t-7=3 \\\\ t=3+7 \\\\ t=10 \\\\\text{OR}\\\\ t-7=-3 \\\\ t=-3+7 \\\\ t=4 .\end{array} Hence, $ t=\left\{ 4,10 \right\} .$
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