Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 1 - Section 1.7 - Absolute Value Equations and Inequalities - 1.7 Exercises: 73


$x=\left\{ -5,1 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ |x+2|=5-2 ,$ 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+2|=3 .\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+2=3 \\\\\text{OR}\\\\ x+2=-3 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} x+2=3 \\\\ x=3-2 \\\\ x=1 \\\\\text{OR}\\\\ x+2=-3 \\\\ x=-3-2 \\\\ x=-5 .\end{array} Hence, $ x=\left\{ -5,1 \right\} .$
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