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Layla B.

asked • 04/02/18

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

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.

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