Question

solve for f and graph the solution. 2f - 11 ≤ 5 or f - 8 ≥ 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

Solve $2f - 11\leq5$. Add 11 to both sides: $2f\leq5 + 11$, so $2f\leq16$. Divide both sides by 2, we get $f\leq8$.

Step2: Solve the second inequality

Solve $f - 8\geq7$. Add 8 to both sides, we have $f\geq7 + 8$, so $f\geq15$.

Step3: Analyze the compound - inequality

The compound inequality is $2f - 11\leq5$ or $f - 8\geq7$, which means $f\leq8$ or $f\geq15$.

Step4: Plot on the number - line

For $f\leq8$, we use a closed - circle at 8 (because the inequality is $\leq$) and draw an arrow to the left. For $f\geq15$, we use a closed - circle at 15 (because the inequality is $\geq$) and draw an arrow to the right.

Answer:

The solution of the inequality is $f\leq8$ or $f\geq15$. On the number - line, we have a closed - circle at 8 with an arrow to the left and a closed - circle at 15 with an arrow to the right.