Answer
$20\lt m$ or $8\gt m$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 3|14-m|\gt18$
Divide each side by $3$.
$\Rightarrow \frac{3|14-m|}{3}\gt\frac{18}{3}$
Simplify.
$\Rightarrow |14-m|\gt6$
Write a compound inequality.
$\Rightarrow 14-m\lt -6$ or $14-m\gt 6$
Add $m+6$ to each side of the first inequality and $m-6$ to each side of the second inequality.
$\Rightarrow 14-m+m+6\lt -6+m+6$ or $14-m+m-6\gt 6+m-6$
Simplify.
$\Rightarrow 20\lt m$ or $8\gt m$
Hence, the solution is $20\lt m$ or $8\gt m$.
