Question

which graph represents the solution set of this inequality?
9 - 4d ≥ -3
choose 1 answer:
a (graph with blue line left from 3)
b (graph with teal line right from 3)

Explanation:

Step1: Solve the inequality for \( d \)

Start with \( 9 - 4d \geq -3 \). Subtract 9 from both sides:
\( 9 - 4d - 9 \geq -3 - 9 \)
Simplify: \( -4d \geq -12 \).

Step2: Divide by -4 (reverse inequality)

Divide both sides by -4 (remember to reverse the inequality sign when dividing by a negative number):
\( \frac{-4d}{-4} \leq \frac{-12}{-4} \)
Simplify: \( d \leq 3 \).

Step3: Analyze the number line graphs

• For \( d \leq 3 \), the graph should have a closed dot at 3 (since \( \leq \) includes 3) and an arrow pointing to the left (toward smaller numbers).
• Graph A has a closed dot at 3 and an arrow left, matching \( d \leq 3 \).
• Graph B has a closed dot at 3 but an arrow right, which would represent \( d \geq 3 \), not our solution.

Answer:

A. The graph with a closed dot at 3 and an arrow pointing left (toward -5, -4, etc.)