If x is not equal to 0, is |x| less than 1?
(1) (x/|x|) < x
(2) |x| > x
1: (x/|x|) < x
if x is +ve and > 1, x/lxl = 1, which is always < x because x > 1. no.
if x is -ve fraction but > -1, x/lxl = -1, which is always < x because x is a -ve fraction > -1. yes.
so not suff..
2: |x| > x
lxl is +ve. to have lxl > x, x has to be -ve but x could be >-1 or <-1. so still not suff.
1&2: x is -ve and > -1.
so x is -ve fraction. suff.