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

Question

Responses

−13.5−13.5

negative 13.5

−12.5−12.5

negative 12.5

−12−12

negative 12

−13

Answer 1

To solve the inequality \(-32.5 - 6b \geq 48.5\), we need to isolate \(b\). Here’s how we can do it step-by-step:

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 an inequality by a negative number, you must reverse the inequality sign: \[ b \leq \frac{81}{-6} \] \[ b \leq -13.5 \]

This means \(b\) must be less than or equal to \(-13.5\). Among the provided options, \(−13.5\) is not included because the inequality is true for values less than or equal to \(-13.5\). Thus, the correct answer must be another value that is less than or equal to \(-13.5\).

The options provided are:

• −13.5
• −12.5
• −12
• −13

The value \( -13.5 \) itself makes the inequality a true statement, as \( -32.5 - 6(-13.5) = 81 \), which satisfies \( 81 \geq 48.5\).

So, the answer is −13.5 (or negative 13.5).