5

Set 6: Linear Inequalities (Intermediate)

Explanation

Answer: B

A streaming platform limits video quality based on internet speed. For HD quality, speed must be at least 5 Mbps. For 4K quality, speed must be at least 25 Mbps. If someone's speed ss qualifies for 4K, which statement is necessarily true?

A.

s<25s < 25

B.

s25s \geq 25

✓ Correct
C.

5s<255 \leq s < 25

D.

s=25s = 25

Detailed Explanation

Choice B is correct. Choice B is the correct answer. Qualifying for a higher tier automatically means meeting that tier's minimum. 1. 4 K requirement: Speed must be at least 25 Mbps 2. Translation: "At least 25" means s25s \geq 25 3. Logic: If someone qualifies for 4 K, their speed MUST be 25\geq 25 Strategic Tip: Meeting a "higher" requirement automatically satisfies all "lower" requirements as well. Choice A is incorrect because s<25s < 25 would NOT qualify for 4 K (contradicts the premise). Choice C is incorrect because this range represents speeds that qualify for HD but NOT 4 K. Choice D is incorrect because s=25s = 25 is the minimum, but 4 K could have any speed 25\geq 25 (like 30, 50, 100 Mbps).

Key Steps:

The correct answer is s25s \geq 25

Why others are wrong:
A: Choice A 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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