If mod x + 4 = 2 then x = ?
1) x^2 not equal to 4
2) x^2 = 36
I have tried solving the question and pretty much through it. I am not sure why option 2 is sufficient along with option 1.
Below is my solution
Case 1 -
|x + 4| = x + 4 = 2 makes x = -2. On back-check answer is consistent with the initial assumption that x + 4 is positive.
When x = -2, x + 4 = 2, which is indeed positive. This means that x = -2 is a good answer.
Case 2 -
x + 4 is negative makes |x + 4| = -x - 4 = 2. This means that -x = 6 or x = -6. Again we back-check: -6 + 4 = -2, which is negative.
So there are two answers to this problem: x = -2 or x = -6.
Now, getting to our stmts:
1. means that x is neither 2 or -2. This eliminates x = -2 and leaves x = -6. So 1 is sufficient.
2. x^2 = 36 makes x as 6 or -6. QUERY - At this point, we are sure that x = -6 corresponds to the main equation answer but how does it eliminate x=-2? It actually gives no infor if x =-2 should be discarded. Should I assume the overlapping value of -6 should be taken in this case? Please advice.