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: 29

Answer

$t=\left\{ -5.5,5.5 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |t|+1.1=6.6 ,$ isolate first the absolute value expression. Then use the definition of an absolute value equality. $\bf{\text{Solution Details:}}$ Using the properties of equality, the given equation is equivalent to \begin{array}{l}\require{cancel} |t|+1.1=6.6 \\\\ |t|=6.6-1.1 \\\\ |t|=5.5 .\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=5.5 \\\\\text{OR}\\\\ t=-5.5 .\end{array} Hence, $ t=\left\{ -5.5,5.5 \right\} .$
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