Question

Which of the following values for b makes the inequality −32.5−6b≥48.5true?(1 point)Responses−13.5 -13.5 −13 -13 −12 -12 −12.5 -12.5

Answer 1

To determine which value of \( b \) makes the inequality \( -32.5 - 6b \geq 48.5 \) true, let's solve the inequality step by step.

1. Start with the inequality:
\[
-32.5 - 6b \geq 48.5
\]

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

3. Simplify the right side:
\[
-6b \geq 81
\]

4. Divide both sides by -6. Remember, when dividing by a negative number, the inequality sign flips:
\[
b \leq -\frac{81}{6}
\]
\[
b \leq -13.5
\]

Now, we need to check which of the given choices satisfies this inequality:

- \( b = -13.5 \) (satisfies \( b \leq -13.5 \))
- \( b = -13 \) (does not satisfy \( b \leq -13.5 \))
- \( b = -12 \) (does not satisfy \( b \leq -13.5 \))
- \( b = -12.5 \) (does not satisfy \( b \leq -13.5 \))

The only value for \( b \) that makes the inequality true is:
- **-13.5**