Is |x|

Question

Is |x| < 1?

(1) |x+1| = 2|x-1|
(2) |x-3| ≠ 0

BG · Answer

Seems like C to me

A) is equivalent to (x-3)*(x-1/3)=0
so x can be 3 or 1/3-INSUFF
B) X is not 3 

 both combined yield X=1/3

then C is suff

shobhitb · Answer

C

for statement to be true -1<x<1

Statement 1

x=1/3 or x=3 ...not true for x=3 hence not sufficient

Statement 2
x not equal to 3..not sufficient as x xan be 4,5 or 1/2 etc 

Together
x=1/3
Hence sufficient

consultinghokie · Answer

question: 

with absolute signs, to find the positive value, we simply drop the absolute signs and solve for x. as in stmt 1, x = 3

so, then, how do we find the negative value of |x+1| = 2|x-1| ? what are the steps?

shampoo · Answer

C aswell.

x=1/3 or x=3, therefore taking both statments x=1/3 suff.

haas_mba07 · Answer

Its C.

With |x+1| = 2|x-1|

we have the following cases:
(after solving for x)
1. x+1 >= 0, x-1 >= 0 ==> x =3
2. x+1 >= 0, x-1 x = 1/3
3. x+1 = 0 ==> No Soln.
4. x+1 x = 3

Without (2) |x-3| != 0, we have two solutions.

Is |x| < 1? (1) |x+1| = 2|x-1| (2) |x-3| ? 0

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