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

Question

Responses

−12.5
negative 12.5

−13.5
negative 13.5

−13
negative 13

−12
negative 12

Answer 1

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

1. First, add \(32.5\) to both sides of the inequality:

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

\[ -6b \geq 81 \]

2. Next, divide both sides by \(-6\). Remember that dividing by a negative number reverses the inequality sign:

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

\[ b \leq -13.5 \]

Now, we need to determine which of the response options are less than or equal to \(-13.5\):

• \(-12.5\): Not less than or equal to \(-13.5\) (too high)
• \(-13.5\): Equal to \(-13.5\) (satisfies the inequality)
• \(-13\): Not less than or equal to \(-13.5\) (too high)
• \(-12\): Not less than or equal to \(-13.5\) (too high)

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

−13.5