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

Answer 1

To solve the inequality \(-32.5 - 6b \geq 48.5\), we first want to isolate \(b\).

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

2. Next, 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 can analyze the choices given:

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

The inequality \(b \leq -13.5\) means \(b\) can be any value less than or equal to \(-13.5\). Among the given choices, the only option that satisfies this condition is:

• \(-13.5\)

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