Set 3: Linear Inequalities (Advanced)

Explanation

Answer: A

A number $n$ is at least 5 and less than 12. Which inequality represents this?

$5 \leq n < 12$

✓ Correct

$5 < n \leq 12$

$5 \leq n \leq 12$

$5 < n < 12$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Translate the phrases to symbols. 1. "At least 5": $n \geq 5$ or $5\leq n$ 2. "Less than 12": $n < 12$ 3. Combine: $5\leq n < 12$ Strategic Tip: Pay close attention to "strict" ( $<, >$ ) vs "inclusive" ( $\leq, \geq$ ) phrases. Choice B is incorrect because it swaps the inclusive/strict conditions. Choice C is incorrect because it includes 12 ("less than or equal to"). Choice D is incorrect because it excludes 5 ("greater than").

Key Steps:

•

The correct answer is $5\leq n < 12$

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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