Set 10: Linear Inequalities (Intermediate)

Explanation

Answer: A

Solve: $2< \frac{3 - x}{2} \leq 4$

$-5 \leq x < -1$

✓ Correct

$-1 < x \leq 5$

$-5 < x \leq -1$

$1 < x \leq 5$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Isolate $x$ . 1. Multiply by 2: $4< 3 - x \leq 8$ 2. Subtract 3: $1< -x \leq 5$ 3. Divide by -1: $-1 > x \geq -5$ (Reverse signs!) 4. Rewrite: $-5 \leq x < -1$ Strategic Tip: When dividing a compound inequality by a negative, the entire order flips. Choice B is incorrect because it fails to reverse signs. Choice C is incorrect because it swaps the strict/inclusive endpoints. Choice D is incorrect because it solves incorrectly.

Key Steps:

•

The correct answer is $-5 \leq x < -1$

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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