Question

which graph represents the solution set of this inequality? 11q + 5 ≤ 49 choose 1 answer: a (number line with blue dot at 4 and arrow to right) b (number line with blue dot at 4 and arrow to left)

Explanation:

Step1: Solve the inequality

Subtract 5 from both sides: $11q + 5 - 5 \leq 49 - 5$ → $11q \leq 44$.
Divide both sides by 11: $\frac{11q}{11} \leq \frac{44}{11}$ → $q \leq 4$.

Step2: Analyze the number line graphs

For $q \leq 4$, the graph should have a closed dot at 4 (since the inequality is "less than or equal to") and the line should extend to the left (towards smaller numbers).

• Graph A has a closed dot at 4 and extends to the right (which would be for $q \geq 4$), so it's incorrect.
• Graph B has a closed dot at 4 and extends to the left, which matches $q \leq 4$.

Answer:

B