Answer
$q=\left\{ -1,1 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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\}
.$
