Question

solve for m and graph the solution.
m - 18 ≥ -12 or 3m - 4 < -7
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Explanation:

Step1: Solve the first inequality

Add 18 to both sides of $m - 18\geq - 12$.
$m-18 + 18\geq - 12+18$
$m\geq6$

Step2: Solve the second inequality

Add 4 to both sides of $3m - 4\lt - 7$.
$3m-4 + 4\lt - 7+4$
$3m\lt - 3$
Then divide both sides by 3: $\frac{3m}{3}\lt\frac{-3}{3}$, so $m\lt - 1$.

Answer:

The solution is $m\lt - 1$ or $m\geq6$. On the number - line, there is an open circle at $m=-1$ (since $m\lt - 1$) and a closed circle at $m = 6$ (since $m\geq6$). The graph has a ray going to the left from $m=-1$ and a ray going to the right from $m = 6$.