Question

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solve for f and graph the solution.
f - 10 > -6 or f + 13 ≤ 13
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 10 to both sides of $f - 10>-6$.
$f-10 + 10>-6 + 10$
$f>4$

Step2: Solve the second inequality

Subtract 13 from both sides of $f + 13\leq13$.
$f+13-13\leq13 - 13$
$f\leq0$

Step3: Graph the solution

The solution of $f>4$ is a ray starting at 4 (open - circle) and going to the right. The solution of $f\leq0$ is a ray starting at 0 (closed - circle) and going to the left.

Answer:

The solution of the compound - inequality is $f\leq0$ or $f>4$. On the number line, there is a closed circle at 0 with a ray going to the left and an open circle at 4 with a ray going to the right.