I cannot comment, so I have to add this down here:
The last: "if x is a positive number" is incorrect. It must've been a result of misinterpretation. So, we usually end up using this in places like this:
As, x can be both 3,-3 simultaneously to give an absolute value of 3, which the inequity doesn't demand. (x should be smaller than absolute value of 3)
This is one answer I'm not understanding. The two 'comments' are contridictory. In the first, |3| < x (Absolute value of 3 is less than x) is pretty straightforward. But is then followed by: -3 < x < 3 (negative 3 is less than x which is less than 3). Huh? Unless these are two completely independent statements, they are contradictory. In the first, x is greater than the absolute value of 3. Which is 3. So if the second comment is intended to be a corollary, shouldn't the value be stated as: -3 < x > 3? And as such is completely redundant, as the first establishes that the value of x is GREATER than the absolute value of 3, which is 3. Thus: x>3 done.
Did I miss something? Absolute value HAS no sign, and in fact DENIES the application OF a sign...
Then, to make it even worse for me, the poster then adds under that 'As, x can be both 3,-3 simultaneously'... What? No, x MUST be a value of LESS than 3 if the second inequity IS intended to be a second statement, AND MUST be GREATER than -3 for the same reason. Thus in the second, x = (-3,3) meaning that the value of x is any number (whole or not) that is greater than -3, and less than 3.
Now if the second IS intended as a corollary to the first, it's totally messed up, as it should then be: -3 < 3 < x and is again, redundant, because any number larger than 3 (|3|) is AUTOMATICALLY larger than -3... thus the most complete answer would be x = [3,+∞)... Or again, did I miss something?