Answer
$3\leq f \leq 9$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 4|f-6|\leq 12$
Divide each side by $4$.
$\Rightarrow \frac{4|f-6|}{4}\leq \frac{12}{4}$
Simplify.
$\Rightarrow |f-6|\leq 3$
Write a compound inequality.
$\Rightarrow f-6\leq 3$ and $f-6\geq -3$
Add $6$ to each side.
$\Rightarrow f-6+6\leq 3+6$ and $f-6+6\geq -3+6$
Simplify.
$\Rightarrow f\leq 9$ and $f\geq 3$
Hence, the solution is $3\leq f \leq 9$.
