If X is negative, is X < -3?
My note: This is a yes/no question. X can be anything negative.
1. X^2 > 9
I took the square root of both sides and got X > +/-3
Since X is negative, the first option (X > +3) is out.
Why is the second option (x > -3) wrong? Why is it not X > -3? I don't understand how the results are x>3 or x < -3. I didn't divide or multiply both sides by a negative number, so I don't understand why the sign changes from X > - 3 to X < -3. Please help me understand this concept. Should I not square both sides here?
Thanks very much.
EDIT: I think I got it. Drawing a number line helps. I tested -4 and it it makes sense and I see it now. I X would be LESS than -3.
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Hi Poisson,
When you're dealing with X^2 > 9, then there are two 'groups' of numbers that fit this information:
X > 3
X < -3
If you don't clearly see why, then you can always come up with a couple of quick examples to prove the math: 4^2 = 16 and (-4)^2 = 16. Since both of those values are greater than 9, both have to be accounted for by the work that you do. 4 > 3 and -4 < -3. Now, just swap out the 4 and -4 for X.
GMAT assassins aren't born, they're made,
Rich
When you're dealing with X^2 > 9, then there are two 'groups' of numbers that fit this information:
X > 3
X < -3
If you don't clearly see why, then you can always come up with a couple of quick examples to prove the math: 4^2 = 16 and (-4)^2 = 16. Since both of those values are greater than 9, both have to be accounted for by the work that you do. 4 > 3 and -4 < -3. Now, just swap out the 4 and -4 for X.
GMAT assassins aren't born, they're made,
Rich
