6

Set 8: Linear Inequalities (Advanced)

Explanation

Answer: A

Solve: 4x+3<114x + 3 < 11 or 2x5>72x - 5 > 7

A.

x<2x < 2 or x>6x > 6

✓ Correct
B.

x<2x < 2 or x>1x > 1

C.

2<x<62 < x < 6

D.

x<3.5x < 3.5 or x>6x > 6

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Solve independently. 1. First: 4x<8x<24x < 8 \rightarrow x < 2 2. Second: 2x>12x>62x > 12 \rightarrow x > 6 3. Combine: x<2x < 2 or x>6x > 6 Strategic Tip: Always simplify each inequality fully before combining. Choice B is incorrect because it solves the second inequality incorrectly (x>1x > 1). Choice C is incorrect because it tries to form an "and" interval. Choice D is incorrect because it solves the first inequality incorrectly.

Key Steps:

The correct answer is x<2x < 2 or x>6x > 6

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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