## Intermediate Algebra (6th Edition)

$x=\left\{ -3,3 \right\}$
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 $x=\left\{ -3,3 \right\} .$