## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$n=\{ -23,23 \}$
$\bf{\text{Solution Outline:}}$ 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, $n=\{ -23,23 \} .$