Algebra-1

The correct option is D. {x|x∈ℝ, x > 2 or x < -2}.

To determine the solution set of the inequality |x| > 2, we need to consider two cases:

Case 1: x is positive (x > 0)
In this case, the inequality |x| > 2 simplifies to x > 2.

Case 2: x is negative (x < 0)
In this case, the inequality |x| > 2 simplifies to -x > 2. By multiplying both sides of the inequality by -1 and reversing the inequality sign, we get x < -2.

Combining both cases, we have the solution set: {x|x∈ℝ, x > 2 or x < -2}. This means that x can be any real number greater than 2 or any real number less than -2.

Let's examine the other options to understand why they are not correct:

A. {x|x∈ℝ, x > 2}: This option suggests that x can be any real number greater than 2. However, in the origin...