Question

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

−12.5
negative 12.5

−13.5
negative 13.5

−13
negative 13

−12
negative 12

Answer 1

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

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

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

\[
-6b \geq 81
\]

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 need to determine which of the response options are less than or equal to \(-13.5\):

- **\(-12.5\)**: Not less than or equal to \(-13.5\) (too high)
- **\(-13.5\)**: Equal to \(-13.5\) (satisfies the inequality)
- **\(-13\)**: Not less than or equal to \(-13.5\) (too high)
- **\(-12\)**: Not less than or equal to \(-13.5\) (too high)

Therefore, the value for \(b\) that makes the inequality true is:

**−13.5**