Answer
$f\lt 3$ or $f\gt 3$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 6|-f+3|+7\gt7$
Subtract $7$ from each side.
$\Rightarrow 6|-f+3|+7-7\gt7-7$
Simplify.
$\Rightarrow 6|-f+3|\gt0$
Divide each side by $6$.
$\Rightarrow \frac{6|-f+3|}{6}\gt\frac{0}{6}$
Simplify.
$\Rightarrow |-f+3|\gt0$
Write a compound inequality.
$\Rightarrow -f+3\lt 0$ or $-f+3\gt 0$
Add $f$ to each side.
$\Rightarrow -f+3+f\lt 0+f$ or $-f+3+f\gt 0+f$
Simplify.
$\Rightarrow 3\lt f$ or $3\gt f$
Hence, the solution is $f\lt 3$ or $f\gt 3$.
