Answer
$\left( -\infty, -\dfrac{7}{2}\right) \cup \left( \dfrac{7}{2},\infty \right)$
Work Step by Step
For any $a\gt0$, $|x|\gt a$ implies $x\gt a \text{ OR } x\lt -a$. (The symbol $\gt$ may be replaced with $\ge$.)
Using the concept above, the solutions to the given inequality, $
|2x|\gt7
,$ is
\begin{array}{l}\require{cancel}
2x\gt7
\\\\
x\gt\dfrac{7}{2}
,\\\\\text{ OR }\\\\
2x\lt-7
\\\\
x\lt-\dfrac{7}{2}
.\end{array}
In interval notation, the solution set is $
\left( -\infty, -\dfrac{7}{2}\right) \cup \left( \dfrac{7}{2},\infty \right)
.$
