7

Set 10: Linear Inequalities (Intermediate)

Explanation

Answer: A

Solve: 3(x+1)93(x + 1) \leq 9 and 2x>42x > -4

A.

2<x2-2 < x \leq 2

✓ Correct
B.

2x2-2 \leq x \leq 2

C.

x2x \leq 2

D.

x>2x > -2

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Solve independently. 1. First: 3x+393x6x23x + 3 \leq 9 \rightarrow 3 x \leq 6 \rightarrow x \leq 2 2. Second: x>2x > -2 3. Combine: x>2x > -2 AND x22<x2x \leq 2 \rightarrow -2 < x \leq 2 Strategic Tip: Pay attention to strict (>>) vs inclusive (\leq) endpoints. Choice B is incorrect because it makes -2 inclusive. Choice C is incorrect because it misses the lower bound. Choice D is incorrect because it misses the upper bound.

Key Steps:

The correct answer is 2<x2-2 < x \leq 2

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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