10
algebra

A data plan allows a maximum of 15 GB per month. After using 8.5 GB, which inequality represents the remaining data dd that can be used?

A

d6.5d \leq 6.5

B

d6.5d \geq 6.5

C

d23.5d \leq 23.5

D

d+8.515d + 8.5 \geq 15

Correct Answer: A

Choice A is the correct answer. This real-world constraint problem models resource allocation with inequalities.

  1. Total usage: 8.5+d8.5 + d must not exceed 15 GB
  2. Set up: 8.5+d158.5 + d \leq 15
  3. Solve: Subtract 8.5: d158.5d \leq 15 - 8.5
  4. Calculate: d6.5d \leq 6.5 GB

?�� Strategic Tip: Maximum capacity problems use \leq to ensure totals don't exceed limits.

Choice B is incorrect because6.5\geq 6.5 would mean using at least 6.5 GB more, which could exceed the 15 GB limit. Choice C is incorrect because it adds 8.5 and 15 instead of subtracting, misunderstanding the constraint. Choice D is incorrect because while structurally close, using \geq reverses the constraint logic.