3

Set 2: Linear Inequalities (Intermediate)

Explanation

Answer: A

Solve: 4x+134x + 1 \leq -3 or x51x - 5 \geq 1

A.

x1x \leq -1 or x6x \geq 6

✓ Correct
B.

x1x \leq -1 or x4x \geq -4

C.

1x6-1 \leq x \leq 6

D.

x4x \leq -4 or x6x \geq 6

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Solve independently. 1. First: 4x4x14x \leq -4 \rightarrow x \leq -1 2. Second: x6x \geq 6 3. Combine: x1x \leq -1 or x6x \geq 6 Strategic Tip: "Or" inequalities usually result in two separate regions. Choice B is incorrect because it solves the second part incorrectly. Choice C is incorrect because it tries to combine disjoint sets with "and". Choice D is incorrect because it solves the first part incorrectly.

Key Steps:

The correct answer is x1x \leq -1 or x6x \geq 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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