Question

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

−12
negative 12

−12.5
negative 12.5

−13
negative 13

−13.5

Answer 1

To find which value for \( b \) makes the inequality \( -32.5 - 6b \geq 48.5 \) true, we first need to solve the inequality for \( b \).

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

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

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

Now we check the answer choices to see which values satisfy \( b \leq -13.5 \):

- \( -12 \): Does not satisfy (it's greater than -13.5)
- \( -12.5 \): Does not satisfy (it's greater than -13.5)
- \( -13 \): Does not satisfy (it's greater than -13.5)
- \( -13.5 \): Satisfies (it is equal to -13.5)

The value of \( b \) that makes the inequality true is **−13.5**.