#### Answer

$n=\{ -23,23 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
2|n|+4=50
,$ isolate first the absolute value expression. Then, use the definition of an absolute value equality to solve for the variable.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
2|n|+4=50
\\\\
2|n|=50-4
\\\\
2|n|=46
\\\\
|n|=\dfrac{46}{2}
\\\\
|n|=23
.\end{array}
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
n=23
\\\\\text{OR}\\\\
n=-23
.\end{array}
Hence, $
n=\{ -23,23 \}
.$