5
algebra

Which inequality has a solution set of ALL real numbers?

A

x>2|x| > -2

B

x<2|x| < -2

C

x>2|x| > 2

D

x<2|x| < 2

Correct Answer: A

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.