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Hi Infymys,
Your approach to solve this question is right and you have reached to the solution.
The answer to this problem is: either (x<2 and x> 2), say R1 or (x>2 and x<2), say R2.
If we consider only integer values, then
R1 = {1, 0, 1} & R2 = {..., 5, 4, 3, 3, 4, 5, ...}
x can be any one of these numbers.
So, possible values of x are {..., 5, 4, 3, 1, 0, 1, 3, 4, 5, ...} For this problem, you can not find a single value of x. The value of x lies in a range.
If you will pick any value in this range, it will satisfy the equation (x  2)(x + 2) < 0
For example, let x=1, then (x  2)(x + 2) = (1  2)(1 + 2) = (1)(3) = 3 (which is less than 0).
For a value, which is not there in the range, (in this case, 2 & 2), it will not satisfy the equation.
When x=2, (x  2)(x + 2) = (2  2)(2 + 2) = (4)(0) = 0 (does not satisfy the equation).
