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

Question

Responses

−12
negative 12

−13.5
negative 13.5

−12.5
negative 12.5

−13
negative 13

Answer 1

To solve the inequality \(-32.5 - 6b \geq 48.5\), we can follow these steps:

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

2. Divide both sides by -6 (remember that when you divide by a negative number, you must flip the inequality sign): \[ b \leq \frac{81}{-6} \] \[ b \leq -13.5 \]

Now we use this result to evaluate the given options:

• \(-12\): Not true because \(-12 > -13.5\)
• \(-13.5\): True because \(-13.5\) is equal to \(-13.5\)
• \(-12.5\): Not true because \(-12.5 > -13.5\)
• \(-13\): Not true because \(-13 > -13.5\)

The only value that makes the inequality true is:

−13.5 (negative 13.5).