Question

for each value of w, determine whether it is a solution to -33 ≥ 7w - 5.

w	is it a solution?
8	yes ○	no ○
9	yes ○	no ○
-4	yes ○	no ○

Explanation:

Step1: Solve the inequality for \( w \)

First, solve \( -33 \geq 7w - 5 \) for \( w \). Add 5 to both sides:
\( -33 + 5 \geq 7w - 5 + 5 \)
\( -28 \geq 7w \)

Then divide both sides by 7:
\( \frac{-28}{7} \geq \frac{7w}{7} \)
\( -4 \geq w \) or \( w \leq -4 \)

Step2: Check \( w = -8 \)

Substitute \( w = -8 \) into \( w \leq -4 \). Since \( -8 \leq -4 \) is true, \( w = -8 \) is a solution.

Step3: Check \( w = 8 \)

Substitute \( w = 8 \) into \( w \leq -4 \). Since \( 8 \leq -4 \) is false, \( w = 8 \) is not a solution.

Step4: Check \( w = 9 \)

Substitute \( w = 9 \) into \( w \leq -4 \). Since \( 9 \leq -4 \) is false, \( w = 9 \) is not a solution.

Step5: Check \( w = -4 \)

Substitute \( w = -4 \) into \( w \leq -4 \). Since \( -4 \leq -4 \) is true, \( w = -4 \) is a solution.

Answer:

• For \( w = -8 \): Yes
• For \( w = 8 \): No
• For \( w = 9 \): No
• For \( w = -4 \): Yes

(To mark the table:

• \( w = -8 \): Select "Yes"
• \( w = 8 \): Select "No"
• \( w = 9 \): Select "No"
• \( w = -4 \): Select "Yes" )