Inequality 6

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.

we r getting 2 values 1 & 1/2 from the 2 statement...on what basis did u eliminate 1/2..

I eliminated 1/2 because we originally assumed x to be negative in case a. Since the resulting x from equation -x = 3x - 2 is not negative, then there is no negative solution to this problem.

If you the above explanation isn't clear, the easiest thing to do is just check your answers. Plug 1/2 in for x and you see it is not the answer.

We could also logically eliminate negative solutions before even trying one out.

Let's examine the 2nd statement:

3x - 2 = |x|

Well, we know that |x| is greater than or equal to 0. Therefore, we can rewrite the statement as:

3x - 2 >= 0

3x >= 2

x >= 2/3

Therefore, x MUST be positive. Since x must be positive, we don't need to worry about the case of x being negative, which means that (2) will have only 1 solution for x: sufficient.