Question

solve the inequality and graph the solution. -3(f - 2) + 18 ≤ 12 plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Expand the left - hand side

-3(f - 2)+18=-3f + 6+18=-3f+24. So the inequality becomes -3f + 24≤12.

Step2: Subtract 24 from both sides

-3f+24 - 24≤12 - 24, which simplifies to -3f≤-12.

Step3: Divide both sides by - 3 and reverse the inequality sign

Since we are dividing by a negative number, the inequality sign flips. So $\frac{-3f}{-3}\geq\frac{-12}{-3}$, which gives f≥4.

Answer:

The solution of the inequality is f≥4. On the number - line, we plot a closed circle at 4 (because the inequality is "greater than or equal to") and draw a ray to the right of 4.