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

Question

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

−12.5
negative 12.5

−13.5
negative 13.5

−13
negative 13

−12

GPT-4o mini · Answer

To solve the inequality $-32.5 - 6b \geq 48.5$, we can isolate $b$. 1. Add $32.5$ to both sides: $$ -6b \geq 48.5 + 32.5 $$ This simplifies to: $$ -6b \geq 81 $$ 2. Now divide both sides by $-6$. Remember that dividing by a negative number reverses the inequality: $$ b \leq -\frac{81}{6} $$ Reducing $-\frac{81}{6}$: $$ -\frac{81}{6} = -13.5 $$ Thus, we find that: $$ b \leq -13.5 $$ Now let's evaluate the answer choices: - $-12.5$: This does not satisfy the inequality ($-12.5 > -13.5$). - $-13.5$: This satisfies the inequality ($-13.5 \leq -13.5$). - $-13$: This does not satisfy the inequality ($-13 > -13.5$). - $-12$: This does not satisfy the inequality ($-12 > -13.5$). The only value for $b$ that makes the inequality true is: $-13.5$.