Question

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

-13
-13

-12
-12

-13.5

Answer 1

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

1. First, let's add 32.5 to both sides of the inequality:

\[
-6b \geq 48.5 + 32.5
\]

Calculating the right side:

\[
48.5 + 32.5 = 81
\]

So the inequality becomes:

\[
-6b \geq 81
\]

2. Next, we divide both sides by -6. Remember, when dividing or multiplying by a negative number, we must flip the inequality sign:

\[
b \leq \frac{81}{-6}
\]

Calculating the fraction:

\[
\frac{81}{-6} = -13.5
\]

So the inequality simplifies to:

\[
b \leq -13.5
\]

This means that \(b\) should be less than or equal to -13.5. Now, we check which of the given options satisfies this condition:

- **-13**: Not less than -13.5 (not a solution).
- **-12**: Not less than -13.5 (not a solution).
- **-13.5**: Equal to -13.5 (this works since it meets the condition).

Thus, the value for \(b\) that makes the inequality true is **-13.5**.