Which of the following values for b makes the inequality −32.5−6b≥48.5

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

1. First, let's add 32.5 to both sides of the inequality:

\[ -6b \geq 48.5 + 32.5 \]

Calculating the right side:

\[ 48.5 + 32.5 = 81 \]

So the inequality becomes:

\[ -6b \geq 81 \]

2. Next, we divide both sides by -6. Remember, when dividing or multiplying by a negative number, we must flip the inequality sign:

\[ b \leq \frac{81}{-6} \]

Calculating the fraction:

\[ \frac{81}{-6} = -13.5 \]

So the inequality simplifies to:

\[ b \leq -13.5 \]

This means that \(b\) should be less than or equal to -13.5. Now, we check which of the given options satisfies this condition:

• -13: Not less than -13.5 (not a solution).
• -12: Not less than -13.5 (not a solution).
• -13.5: Equal to -13.5 (this works since it meets the condition).

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