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

Question

Responses

−13.5
negative 13.5
−12.5
negative 12.5
−13
negative 13
−12

Answer 1

To solve the inequality \(-32.5 - 6b \geq 48.5\), we can isolate \(b\) as follows:

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

2. Divide both sides by \(-6\). Remember that dividing by a negative number reverses the inequality sign: \[ b \leq \frac{81}{-6} \] \[ b \leq -13.5 \]

Now, we need to determine which of the provided values for \(b\) satisfy the inequality \(b \leq -13.5\):

• \(-13.5\) (is equal to \(-13.5\), so it satisfies the inequality)
• \(-12.5\) (is greater than \(-13.5\), does not satisfy)
• \(-13\) (is greater than \(-13.5\), does not satisfy)
• \(-12\) (is greater than \(-13.5\), does not satisfy)

Thus, the only value that makes the inequality true is \(-13.5\).

Therefore, the correct response is −13.5.