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

Answer 1

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

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

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

Now, we can compare the options you provided:

- \( -12.5 \)
- \( -13.5 \)
- \( -13 \)
- \( -12 \)

The values of \(b\) that satisfy the inequality \(b \leq -13.5\) are \(b = -13.5\) or any value less than \(-13.5\). Therefore, the value of \(b\) that makes the inequality true is:

**−13.5 (negative 13.5)**