To solve the inequality \(-32.5 - 6b \geq 48.5\), we first isolate \(b\).
- Add \(32.5\) to both sides:
\[ -6b \geq 48.5 + 32.5 \]
- Calculate the right-hand side:
\[ -6b \geq 81 \]
- Now, divide both sides by \(-6\). Remember that when dividing or multiplying by a negative number, the inequality sign changes direction:
\[ b \leq -\frac{81}{6} \]
- Simplifying \(-\frac{81}{6}\):
\[ b \leq -13.5 \]
This means \(b\) can be any value less than or equal to \(-13.5\).
Now, let's check the given choices:
- −13.5: This value satisfies \(b \leq -13.5\).
- −12: This value does not satisfy \(b \leq -13.5\).
- −12.5: This value does not satisfy \(b \leq -13.5\).
- −13: This value does not satisfy \(b \leq -13.5\).
Therefore, the only choice that makes the inequality true is:
−13.5