8

Set 2: Linear Inequalities (Intermediate)

Explanation

Answer: A

Solve: 2x+1>52x + 1 > 5 or 2x+1<52x + 1 < -5

A.

x>2x > 2 or x<3x < -3

✓ Correct
B.

x>2x > 2 or x<2x < -2

C.

3<x<2-3 < x < 2

D.

x>3x > 3 or x<3x < -3

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Solve each part. 1. Part 1: 2x>4x>22x > 4 \rightarrow x > 2 2. Part 2: 2x<6x<32x < -6 \rightarrow x < -3 3. Combine: x>2x > 2 or x<3x < -3 Strategic Tip: This is equivalent to solving 2x+1>5|2 x+1| > 5. Choice B is incorrect because it solves the second part incorrectly. Choice C is incorrect because it tries to form an "and" interval. Choice D is incorrect because it solves the first part incorrectly.

Key Steps:

The correct answer is x>2x > 2 or x<3x < -3

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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