Which of the following values for b makes the inequality −32.5−6b≥48.5 true?(1 point)

Question

Responses

−12
negative 12

−12.5
negative 12.5

−13
negative 13

−13.5

Answer 1

To find which value for \( b \) makes the inequality \( -32.5 - 6b \geq 48.5 \) true, we first need to solve the inequality for \( b \).

1. Start with the inequality: \[ -32.5 - 6b \geq 48.5 \]

2. Add \( 32.5 \) to both sides: \[ -6b \geq 48.5 + 32.5 \] \[ -6b \geq 81 \]

3. Divide both sides by \( -6 \). Remember that when you divide by a negative number, you need to reverse the inequality sign: \[ b \leq \frac{81}{-6} \] \[ b \leq -13.5 \]

Now we check the answer choices to see which values satisfy \( b \leq -13.5 \):

• \( -12 \): Does not satisfy (it's greater than -13.5)
• \( -12.5 \): Does not satisfy (it's greater than -13.5)
• \( -13 \): Does not satisfy (it's greater than -13.5)
• \( -13.5 \): Satisfies (it is equal to -13.5)

The value of \( b \) that makes the inequality true is −13.5.