Which of the following values for b makes the inequality −32.5−6b≥48.5

Question

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

−13
negative 13

−13.5
negative 13.5

−12
negative 12

−12.5

GPT-4o mini · Answer

To find which value of $ b $ makes the inequality $ -32.5 - 6b \geq 48.5 $ true, we first need to solve the inequality for $ b $. 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. Now divide both sides by $ -6 $. Remember that when you divide or multiply by a negative number, you must reverse the inequality sign: $$ b \leq \frac{81}{-6} $$ $$ b \leq -13.5 $$ Now, we will check which of the provided options is less than or equal to $ -13.5 $: - $ -13 $: is greater than $ -13.5 $ (not true) - $ -13.5 $: is equal to $ -13.5 $ (true) - $ -12 $: is greater than $ -13.5 $ (not true) - $ -12.5 $: is greater than $ -13.5 $ (not true) Therefore, the only value that satisfies the inequality is: **−13.5** (negative 13.5)