Question

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solve for h and graph the solution.
h - 7 ≤ -8 or h + 4 ≥ 9
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 7 to both sides of $h - 7\leq - 8$.
$h-7 + 7\leq - 8+7$
$h\leq - 1$

Step2: Solve the second inequality

Subtract 4 from both sides of $h + 4\geq9$.
$h+4 - 4\geq9 - 4$
$h\geq5$

Step3: Graph the solution

For $h\leq - 1$, we have a closed - circle at $h=-1$ (since the inequality is $\leq$) and an arrow pointing to the left. For $h\geq5$, we have a closed - circle at $h = 5$ (since the inequality is $\geq$) and an arrow pointing to the right.

Answer:

The solution is $h\leq - 1$ or $h\geq5$. On the number - line, there is a closed circle at $h=-1$ with an arrow to the left and a closed circle at $h = 5$ with an arrow to the right.