Question

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

−12
negative 12

−13.5
negative 13.5

−12.5
negative 12.5

−13
negative 13

Answer 1

To solve the inequality \(-32.5 - 6b \geq 48.5\), we can follow these steps:

1. **Add 32.5 to both sides:**
\[
-6b \geq 48.5 + 32.5
\]
\[
-6b \geq 81
\]

2. **Divide both sides by -6** (remember that when you divide by a negative number, you must flip the inequality sign):
\[
b \leq \frac{81}{-6}
\]
\[
b \leq -13.5
\]

Now we use this result to evaluate the given options:

- \(-12\): Not true because \(-12 > -13.5\)
- \(-13.5\): True because \(-13.5\) is equal to \(-13.5\)
- \(-12.5\): Not true because \(-12.5 > -13.5\)
- \(-13\): Not true because \(-13 > -13.5\)

The only value that makes the inequality true is:

**−13.5** (negative 13.5).