Answer
$1\lt n \lt \frac{7}{2}$ The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow |9-4n|\lt 5$
Write a compound inequality.
$\Rightarrow 9-4n\lt 5$ and $9-4n\gt -5$
Add $4n-5$ to each side of first inequality and $4n+5$ to each side of second inequality.
$\Rightarrow 9-4n+4n-5\lt 5+4n-5$ and $9-4n+4n+5\gt -5+4n+5$
Simplify.
$\Rightarrow 4\lt 4n$ and $14\gt 4n$
Divide each side by $4$.
$\Rightarrow \frac{4}{4}\lt \frac{4n}{4}$ and $\frac{14}{4}\gt \frac{4n}{4}$
Simplify.
$\Rightarrow 1\lt n$ and $\frac{7}{2}\gt n$
Hence, the solution is $1\lt n \lt \frac{7}{2}$.
