## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 1 - Section 1.7 - Absolute Value Equations and Inequalities - 1.7 Exercises - Page 119: 74

#### Answer

$x=\left\{ -13,7 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $|x+3|=12-2 ,$ simplify first the right side. Then use the definition of absolute value equality. Use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Simplifying the right side, the given equation is equivalent to \begin{array}{l}\require{cancel} |x+3|=10 .\end{array} 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} x+3=10 \\\\\text{OR}\\\\ x+3=-10 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} x+3=10 \\\\ x=10-3 \\\\ x=7 \\\\\text{OR}\\\\ x+3=-10 \\\\ x=-10-3 \\\\ x=-13 .\end{array} Hence, $x=\left\{ -13,7 \right\} .$

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