Question

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

(1 point)
Responses

-13
-13

-12
-12

-12.5
-12.5

-13.5

Answer 1

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

1. First, add 32.5 to both sides:
\[
-6b \geq 48.5 + 32.5
\]
\[
-6b \geq 81
\]

2. Next, divide both sides by -6. Remember that when you divide by a negative number, the inequality sign flips:
\[
b \leq \frac{81}{-6}
\]
\[
b \leq -13.5
\]

Now we can check the given options:

- **-13**: This is NOT less than or equal to -13.5, so this will NOT satisfy the inequality.
- **-12**: This is NOT less than or equal to -13.5, so this will NOT satisfy the inequality.
- **-12.5**: This is NOT less than or equal to -13.5, so this will NOT satisfy the inequality.
- **-13.5**: This is equal to -13.5, which satisfies the inequality.

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

**-13.5**