Which of the following values for b makes the inequality −32.5−6b≥48.5 true?(1 point) Responses −13.5 negative 13.5 −13 negative 13 −12 negative 12 −12.5

Answer 1

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

1. Start with the original 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, when dividing by a negative number, the inequality sign flips: \[ b \leq \frac{81}{-6} \] \[ b \leq -13.5 \]

So, for the inequality \( -32.5 - 6b \geq 48.5 \) to be true, \( b \) must be less than or equal to \( -13.5 \).

From the provided options:

• \( -13.5 \)
• \( -13 \)
• \( -12 \)
• \( -12.5 \)

The only value that satisfies \( b \leq -13.5 \) is \( -13.5 \).

Thus, the correct answer is: \[ \text{-13.5} \]