Chapter 9 - Inequalities and Problem Solving - 9.3 Absolute-Value Equations and Inequalities - 9.3 Exercise Set - Page 599: 16

x={ -5,5 }

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $|x|=5 ,$ use the definition of an absolute value equality. $\bf{\text{Solution Details:}}$ 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} x=5 \\\\\text{OR}\\\\ x=-5 .\end{array} Hence, $x=\{ -5,5 \} .$

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