Is |x|

Question

Is |x| < 1?

(1) |x+1| = 2|x-1|
(2) |x-3| ≠ 0

bkk145 · Answer

C.

(1) |x+1| = 2*|x-1|
x = 3 or x=1/3
INSUFFICIENT

(2) x ≠ 3
INSUFFICIENT

Together, x=1/3
SUFFICIENT

young_gun · Answer

bkk, do you think you could show me how in (1) you solved x=3 or x=1/3? I'm not too great with abs values. Thanks!

FN · Answer

C...

1) says x can be 3 or 1/3

3) says x cant be 3..or -3 we dont know..

together..yes..

x=1/3

young_gun · Answer

can you explain how you got the bold? thx

bkk145 · Answer

Sure, you have |x+1| = 2*|x-1| You know that |x+1| is positive when x>-1 and negative when x<-1 |x-1| is positive when x>1 and negative when x<1 This means that in a number line, the intervals you have are: x<-1, -11 Now, solve the equation according to those intervals: For x<-1, -x-1 = 2*(-x+1) -x-1 = -2x+2 x = 3 For -11 x+1 = 2*(x-1) x+1 = 2x-2 x = 3 x equals to 3 or 1/3 I know, all these signs are confusing! I attached a document for you, take a look. It helped me.

GMAT TIGER · Answer

1: |x+1| = 2|x-1|
if x is +ve:
x + 1 = 2x - 2
x = 3

if x is -ve:
x + 1 = -2x + 2
x = 1/3

so insufff.

2: if (x-3) is not equal to 0, then x is not 3 but do not know whether x is > than or < 3. NSF

1 & 2: x = 1/3. suff.

C.

kyatin · Answer

bkk145.

Kudos for the doc

Thanks all for clarifications.

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

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