Question

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

−13
negative 13

−13.5
negative 13.5

−12
negative 12

−12.5

Answer 1

To solve the inequality \(-32.5 - 6b \geq 48.5\), we can start by isolating the term that involves \(b\).

1. First, add \(32.5\) to both sides:

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

2. Simplifying the right side:

\[
-6b \geq 81
\]

3. Next, divide both sides by \(-6\). Remember that when you divide or multiply an inequality by a negative number, you need to flip the inequality sign:

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

4. Simplifying \(\frac{81}{-6}\):

\[
b \leq -13.5
\]

This means that any value of \(b\) that is less than or equal to \(-13.5\) will satisfy the original inequality.

Now, we can evaluate the given options:

- **−13**: This is greater than \(-13.5\), so it does not satisfy the inequality.
- **−13.5**: This is equal to \(-13.5\), so it does satisfy the inequality.
- **−12**: This is greater than \(-13.5\), so it does not satisfy the inequality.
- **−12.5**: This is greater than \(-13.5\), so it does not satisfy the inequality.

The value that makes the inequality true is **−13.5**.