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 \(2f\leq16\). Then 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 \(f\geq15\).

Answer:

The solution is \(f\leq8\) or \(f\geq15\). On a number - line, for \(f\leq8\), we have a ray starting from 8 and going to the left (with a closed circle at 8 if the inequality is non - strict). For \(f\geq15\), we have a ray starting from 15 and going to the right (with a closed circle at 15 if the inequality is non - strict).