Precalc question - please help! What's wrong with this answer?

Question

The question is:

 

A student was given the problem: "Solve x² > 4" The student wrote the following response:

STEP 1: x² > 4

STEP 2: √x² > ±√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.

Answer 1

x² > 4

 

When you put in the negative... the inequality must be reversed

 

x>√4 or x<-√4

 

x>2 or x<-2

 

(-∞, -2) U (2, ∞)