Answer
The solutions are $n=5$ and $n=3$.
Work Step by Step
The given equation is
$\Rightarrow |4n-15|=|n|$
Write the two related linear equations.
$4n-15=n$ ...... (1)
$4n-15=-n$ ...... (2)
Solve equation (1).
$\Rightarrow 4n-15=n$
Add $15-n$ to each side.
$\Rightarrow 4n-15+15-n=n+15-n$
Simplify.
$\Rightarrow 3n=15$
Divide each side by $3$.
$\Rightarrow \frac{3n}{3}=\frac{15}{3}$
Simplify.
$\Rightarrow n=5$
Check : $n=5$
$\Rightarrow |4n-15|=|n|$
$\Rightarrow |4(5)-15|=|5|$
$\Rightarrow |20-15|=|5|$
$\Rightarrow |5|=|5|$
True.
Solve equation (2).
$\Rightarrow 4n-15=-n$
Add $15+n$ to each side.
$\Rightarrow 4n-15+15+n=-n+15+n$
Simplify.
$\Rightarrow 5n=15$
Divide each side by $5$.
$\Rightarrow \frac{5n}{5}=\frac{15}{5}$
Simplify.
$\Rightarrow n=3$
Check : $n=3$
$\Rightarrow |4n-15|=|n|$
$\Rightarrow |4(3)-15|=|3|$
$\Rightarrow |12-15|=|3|$
$\Rightarrow |3|=|3|$
True.
Hence, the solutions are $n=5$ and $n=3$.
