7

Set 3: Linear Inequalities

Explanation

Answer: A

Solve: 2x>5|2x| > -5

A.

All real numbers

✓ Correct
B.

No solution

C.

x>2.5x > -2.5

D.

x<2.5x < 2.5

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Analyze the properties of absolute value. 1. Property: 2x0|2 x| \geq 0 for all real xx. 2. Comparison: Is a non-negative number always greater than -5? Yes. 3. Conclusion: True for all real numbers. Strategic Tip: If A>negative|A| > \text{negative}, the answer is always All Real Numbers. Choice B is incorrect because it is always true. Choice C is incorrect because it implies a restriction. Choice D is incorrect because it implies a restriction.

Key Steps:

The correct answer is All real numbers

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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