Question

which of the q-values satisfy the following inequality?
6 - 3q ≤ 1
choose all answers that apply:
a q = 0
b q = 1
c q = 2

Explanation:

Step1: Solve the inequality for \( q \)

Start with the inequality \( 6 - 3q \leq 1 \). Subtract 6 from both sides:
\( 6 - 3q - 6 \leq 1 - 6 \)
Simplify: \( -3q \leq -5 \).

Divide both sides by -3 (remember to reverse the inequality sign when dividing by a negative number):
\( q \geq \frac{5}{3} \approx 1.67 \).

Step2: Check each option

• Option A (\( q = 0 \)): \( 0 \geq \frac{5}{3} \)? No, \( 0 < 1.67 \).
• Option B (\( q = 1 \)): \( 1 \geq \frac{5}{3} \)? No, \( 1 < 1.67 \).
• Option C (\( q = 2 \)): \( 2 \geq \frac{5}{3} \)? Yes, \( 2 \approx 2 \geq 1.67 \).

Answer:

C. \( q = 2 \)