The question is:

A student was given the problem: "Solve x^{2} > 4" The student wrote the following response:

STEP 1: x^{2} > 4

STEP 2: √x^{2} > ±√4

STEP 3: x > ± 2

STEP 4: So, the solution is (-2, ∝) U (2, ∝)

STEP 5: Which is the same as (-2, ∝)

What is wrong with it? Indicate the STEP(S) that are incorrect and explain why they are incorrect.

I am thinking that Step 5 is incorrect because there should be a "hole" at positive 2, because x > 2, but it isn't equal to 2. However, I don't know if this is right because if x > -2, then shouldn't positive 2 also be included in the graph?

Any help would be greatly appreciated!

Note: The symbol "√" is a square root symbol and the "∞" is infinity. I don't know why these formatted oddly.