## Intermediate Algebra: Connecting Concepts through Application

$x=\{ -12,12 \}$
$\bf{\text{Solution Outline:}}$ Use the definition of absolute value equality to solve the given equation, $|x|=12 .$ 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} x=12 \\\\\text{OR}\\\\ x=-12 .\end{array} If $x=12,$ then \begin{array}{l}\require{cancel} |12|=12 \\\\ 12=12 \text{ (TRUE)} .\end{array} If $x=-12,$ then \begin{array}{l}\require{cancel} |-12|=12 \\\\ 12=12 \text{ (TRUE)} .\end{array} Hence, $x=\{ -12,12 \} .$