(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠0
------------------------------------------------------
Given |x|< 1
i.e x<1 and x>-1 i.e basically the question
"Is whether or not -1<x<1"
Now using the choices given --
(1) |x + 1| = 2|x - 1|
Case I :: x+1=2x-2 ---> x=3
------
Case II :: -(x + 1)=2(x - 1) ---> -x-1=2x-2
------- i.e 3x=1 --> x=1/3
Case III :: (x + 1)=2(x - 1)
-------- Same as case I ...which implies x=3
Case IV :: (x + 1)=-2(x - 1)
------- x+1=-2x+2 ---> 3x=1 therefore x=1/3
Using the values of x found above i.e 3(no it doesnt lie in the range -1<x<1) and 1/3(yes it lies in the range asked in the question -1<x<1) the answer to the question can either be a yes or no..we are not sure !!
Thus Not Sufficient.
(2) |x - 3| ≠0
Using this --> x-3 ≠0
i.e x ≠3
or -(x - 3) ≠0
-x+3 ≠0
which implies x ≠3
this gives us a infinte value of x which is possible.
Thus not sufficient.
Using 1 and 2
We can defintely answer the question coz we are limited to x = 1/3
Thus Both together is sufficent. !!!
I hope i made sense...!! any comment anyone ?
