Q- what is x?
1) |x|<2
2)|x|=3x-2
OA b
can someone tell me how to deal with absolute value questions
1) |x|<2
2)|x|=3x-2
OA b
can someone tell me how to deal with absolute value questions
1. Now since |x| < 2, this means that - 2 < x < 2. There are plenty of values between -2 and 2, so you can't guess x.
2. |x| = 3x - 2. As I've always said, this type of question must be broken down in two cases:
a. x < 0, when |x| = -x. This means that -x = 3x - 2, or that 4x - 2 = 0 or that x = 2/4 = 1/2. We must CHECK to see if x = 1/2 is consistent with our initial assumption, that x < 0. And it isn't! This means that there is no negative x to fulfill the requirements.
b. x is positive or equal to 0, when |x| = x. This takes us to x = 3x - 2, or 2x - 2 = 0. x = 1 and, after, checking with the initial assumption, we find that this solution is ok.
So in the end stmt 2 gives us only 1 solution and that is x = 1.
So B is the answer.
