Set 11: Linear Inequalities

Explanation

Answer: A

Solve: $5< 2x + 1 \leq 11$

$2 < x \leq 5$

✓ Correct

$2 \leq x < 5$

$3 < x \leq 6$

$x \leq 5$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Isolate $x$ . 1. Subtract 1: $4< 2 x \leq 10$ 2. Divide by 2: $2< x \leq 5$ Strategic Tip: Maintain the strict ( $<$ ) and inclusive ( $\leq$ ) signs exactly as they are. Choice B is incorrect because it swaps the signs. Choice C is incorrect because it solves incorrectly. Choice D is incorrect because it misses the lower bound.

Key Steps:

•

The correct answer is $2< x \leq 5$

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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