9

Set 6: Linear Inequalities (Intermediate)

Explanation

Answer: A

Which inequality has a solution set of ALL real numbers?

A.

x>2|x| > -2

✓ Correct
B.

x<2|x| < -2

C.

x>2|x| > 2

D.

x<2|x| < 2

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Absolute value is always non-negative (geq0\\geq 0). 1. Logic: x0|x| \geq 0 for any real number. 2. Comparison: Is a non-negative number always greater than -2? Yes. 3. Result: All real numbers. Strategic Tip: Absolute value cannot be negative. x<negative|x| < \text{negative} is impossible (No Solution). x>negative|x| > \text{negative} is always true. Choice B is incorrect because it has No Solution. Choice C is incorrect because it excludes numbers between -2 and 2. Choice D is incorrect because it excludes numbers outside -2 and 2.

Key Steps:

The correct answer is x>2|x| > -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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