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

Question

Responses

−13.5
negative 13.5

−12.5
negative 12.5

−12
negative 12

−13

Answer 1

To solve the inequality \(-32.5 - 6b \geq 48.5\), let's isolate \(b\).

1. Start by adding \(32.5\) 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:

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

Calculating \(\frac{81}{-6}\):

\[ b \leq -13.5 \]

This means that \(b\) must be less than or equal to \(-13.5\).

Now, let's evaluate the response options given:

• \(-13.5\) is equal to \(-13.5\), which satisfies the inequality (b is less than or equal to -13.5).
• \(-12.5\) is greater than \(-13.5\), which does not satisfy the inequality.
• \(-12\) is greater than \(-13.5\), which does not satisfy the inequality.
• \(-13\) is greater than \(-13.5\), which does not satisfy the inequality.

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

\(-13.5\)