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
negative 12

−12.5
negative 12.5

−13

Answer 1

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

1. Add \(32.5\) to both sides:

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

2. Calculate the right-hand side:

\[ -6b \geq 81 \]

3. Now, divide both sides by \(-6\). Remember that when dividing or multiplying by a negative number, the inequality sign changes direction:

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

4. 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:

1. −13.5: This value satisfies \(b \leq -13.5\).
2. −12: This value does not satisfy \(b \leq -13.5\).
3. −12.5: This value does not satisfy \(b \leq -13.5\).
4. −13: This value does not satisfy \(b \leq -13.5\).

Therefore, the only choice that makes the inequality true is:

−13.5