Answer
$x=\left\{ -3,3 \right\}$
Work Step by Step
Using the properties of equality, the given expression, $
\left| 7x \right|-26=-5
,$ is equivalent to
\begin{array}{l}\require{cancel}
\left| 7x \right|=-5+26
\\\\
\left| 7x \right|=21
.\end{array}
Since for any $a\gt0$, $|x|=a$ implies $x=a\text{ or } x=-a$, then the expression, $
\left| 7x \right|=21
,$ is equivalent to
\begin{array}{l}\require{cancel}
7x=21
\\\\
x=\dfrac{21}{7}
\\\\
x=3
,\\\\\text{ OR }\\\\
7x=-21
\\\\
x=-\dfrac{21}{7}
\\\\
x=-3
.\end{array}
Hence, the solution set is $
x=\left\{ -3,3 \right\}
.$
