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joanjgonzalez
- Junior | Next Rank: 30 Posts
- Posts: 11
- Joined: Fri Nov 21, 2008 7:02 am
Solving this question requires us to first recognize the 4 situations in which two absolute values can equal each other. I'll show this with 4 examples:
|4|=|4| both values inside are already positive
|4|=|4| both values inside are negative
|-4|=|4| one value is negative and the other is positive
|4|=|-4| one value is positive and the other is negative
So, (1) gives us 4 possible situations:
a. x+2 = x-3 (both sides already yield positive outcomes)
b. -(x+2) = -(x-3) (both sides yield negative outcomes, which we "undo" or make positive, by negating both sides, which is the same as finding the abs value of each side)
c. -(x+2) = x-3 (the left side yields a negative outcome, which we "undo" by negating)
d. x+2 = -(x-3) (the right side yields a negative outcome, which we "undo" by negating)
Note: c is actually impossible since it could never be the case that x+2 is negative while x-3 is positive, but it doesn't really matter here.
If we solve each of the 4 equations we find that a and b cannot be solved. c and d yield x=1/2
Since x=1/2, we can conclude that (1) is sufficient.
(2) is not sufficient.
Answer: A
