## Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole

# Chapter 2 - Systems of Linear Equations and Inequalities - 2.5 Absolute Value Equations and Inequalities - 2.5 Exercises - Page 186: 4

#### Answer

$m=\{ -20,2 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the definition of absolute value equality to solve the given equation, $|m+9|=11 .$ Do checking of the solution/s. $\bf{\text{Solution Details:}}$ Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to \begin{array}{l}\require{cancel} m+9=11 \\\\\text{OR}\\\\ m+9=-11 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} m+9=11 \\\\ m=11-9 \\\\ m=2 \\\\\text{OR}\\\\ m+9=-11 \\\\ m=-11-9 \\\\ m=-20 .\end{array} If $m=2,$ then \begin{array}{l}\require{cancel} |m+9|=11? \\\\ |2+9|=11? \\\\ |11|=11? \\\\ 11=11 \text{ (TRUE)} .\end{array} If $m=-20,$ then \begin{array}{l}\require{cancel} |m+9|=11? \\\\ |-20+9|=11? \\\\ |-11|=11? \\\\ 11=11 \text{ (TRUE)} .\end{array} Hence, $m=\{ -20,2 \} .$

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