Question

match the inequality with its graph. 3(2 - f) ≤ 15

Explanation:

Step1: Expand the left - hand side

$3(2 - f)=6 - 3f$, so the inequality becomes $6 - 3f\leq15$.

Step2: Subtract 6 from both sides

$6-3f - 6\leq15 - 6$, which simplifies to $-3f\leq9$.

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

Since dividing by a negative number reverses the inequality sign, $\frac{-3f}{-3}\geq\frac{9}{-3}$, so $f\geq - 3$.

Answer:

The graph with a closed - circle at $-3$ and the line extending to the right. (The fourth option among the given graphs as it has a closed - dot at $-3$ and the arrow goes to the right on the number line.)