3

Set 2: Linear Inequalities

Explanation

Answer: A

A cell phone plan includes 2000 text messages per month. After sending 1450 messages, which inequality represents the number of messages tt that can still be sent?

A.

t550t \leq 550

✓ Correct
B.

t550t \geq 550

C.

t3450t \leq 3450

D.

t+14502000t + 1450 \geq 2000

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Resource limit problems model remaining capacity after partial use. 1. Total limit: 2000 messages maximum 2. Already used: 1450 messages 3. Remaining: t+14502000t + 1450 \leq 2000 4. Solve: t20001450=550t \leq 2000 - 1450 = 550 Strategic Tip: "Remaining" or "left over" problems subtract what's used from the total limit. Choice B is incorrect because 550\geq 550 would mean sending at least 550 more, which could exceed the 2000 limit. Choice C is incorrect because it adds 1450 and 2000 instead of subtracting. Choice D is incorrect because while the setup is close, using \geq reverses the constraint logic.

Key Steps:

The correct answer is t550t \leq 550

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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