Question

for each value of v, determine whether it is a solution to 4 + 9v < -32.

v	is it a solution?
8	∘ (yes)	∘ (no)
-8	∘ (yes)	∘ (no)
-4	∘ (yes)	∘ (no)

Explanation:

Step1: Solve the inequality for \( v \)

First, we solve the inequality \( 4 + 9v < -32 \). Subtract 4 from both sides:
\( 9v < -32 - 4 \)
\( 9v < -36 \)
Then divide both sides by 9:
\( v < -4 \)

Step2: Check each value of \( v \)

• For \( v = 7 \): \( 7 \) is not less than \( -4 \), so it is not a solution.
• For \( v = 8 \): \( 8 \) is not less than \( -4 \), so it is not a solution.
• For \( v = -8 \): \( -8 \) is less than \( -4 \), so it is a solution.
• For \( v = -4 \): \( -4 \) is not less than \( -4 \) (it is equal), so it is not a solution.

Answer:

• \( v = 7 \): No
• \( v = 8 \): No
• \( v = -8 \): Yes
• \( v = -4 \): No

(To mark the table: For \( 7 \), select "No"; for \( 8 \), select "No"; for \( -8 \), select "Yes"; for \( -4 \), select "No".)