Question

1. solve and graph.

3t - 12 ≤ -9
a. t ≥ -7
number line with dot at -7 and arrow to right

b. t ≤ -7
number line with dot at -7 and arrow to left

c. t ≥ 1
number line with dot at 1 and arrow to right

d. t ≤ 1
number line with dot at 1 and arrow to left

Explanation:

Step1: Solve the inequality

Start with the inequality \(3t - 12 \leq -9\). Add 12 to both sides: \(3t - 12 + 12 \leq -9 + 12\), which simplifies to \(3t \leq 3\). Then divide both sides by 3: \(\frac{3t}{3} \leq \frac{3}{3}\), so \(t \leq 1\).

Step2: Analyze the graph

For the inequality \(t \leq 1\), the graph should have a closed dot at 1 (since the inequality is "less than or equal to") and the arrow pointing to the left (indicating all values less than or equal to 1). Looking at the options, option D has \(t \leq 1\) and the corresponding graph (arrow left with dot at 1, though the graph's numbering seems a bit off in the image but the inequality matches).

Answer:

D. \( t \leq 1 \)