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: 37

Answer

$m=\left\{ -2,12 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |5-m|+9=16 ,$ isolate first the absolute value expression. Then use the definition of 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} |5-m|+9=16 \\\\ |5-m|=16-9 \\\\ |5-m|=7 .\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} 5-m=7 \\\\\text{OR}\\\\ 5-m=-7 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 5-m=7 \\\\ -m=7-5 \\\\ -m=2 \\\\ m=-2 \\\\\text{OR}\\\\ 5-m=-7 \\\\ -m=-7-5 \\\\ -m=-12 \\\\ m=12 .\end{array} Hence, $ m=\left\{ -2,12 \right\} .$
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