Answer
$n=\{ -5,5 \}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
3|n|+10=25
,$ 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 given expression is equivalent to
\begin{array}{l}\require{cancel}
3|n|+10=25
\\\\
3|n|=25-10
\\\\
3|n|=15
\\\\
|n|=\dfrac{15}{3}
\\\\
|n|=5
.\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=5
\\\\\text{OR}\\\\
n=-5
.\end{array}
Hence, $
n=\{ -5,5 \}
.$
