## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$q=\left\{ -1,1 \right\}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $7|q|+2=9 ,$ isolate first the absolute value expression. Then use the definition of an absolute value equality. $\bf{\text{Solution Details:}}$ Using the properties of equality, the given equation is equivalent to \begin{array}{l}\require{cancel} 7|q|+2=9 \\\\ 7|q|=9-2 \\\\ 7|q|=7 \\\\ |q|=\dfrac{7}{7} \\\\ |q|=1 .\end{array} 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} q=1 \\\\\text{OR}\\\\ q=-1 .\end{array} Hence, $q=\left\{ -1,1 \right\} .$