Chapter 9 - Inequalities and Problem Solving - Review Exercises: Chapter 9: 32

$x=\{ 5,11 \}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $|x-8|=3 ,$ use the definition of an absolute value equality. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ 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} x-8=3 \\\\\text{OR}\\\\ x-8=-3 .\end{array} Using the properties of equality to isolate the variable in each equation results to \begin{array}{l}\require{cancel} x-8=3 \\\\ x=3+8 \\\\ x=11 \\\\\text{OR}\\\\ x-8=-3 \\\\ x=-3+8 \\\\ x=5 .\end{array} Hence, $x=\{ 5,11 \} .$

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