x / |x| < x

[clawhammer]

Please assist with my understanding:

if, x / |x| < x, then how should I rephrase the equation when x is negative?

(A) x / -x > x
or, (B) x / -x < x

[Rahul@gurome]

Please assist with my understanding:

if, x / |x| < x, then how should I rephrase the equation when x is negative?

(A) x / -x > x
or, (B) x / -x < x

Choice B, i.e. x/|x| < x => x/(-x) < x
Because here you're just putting the value of |x|.
Only when both side of an inequality is multiplied with a negative number, the inequality sign reverses.

In this particular question this confusion shouldn't arise at all because x/|x| is equal to 1 for positive x and -1 for negative x. Just replace x/|x| with 1 or -1 for positive or negative analysis.

[clawhammer]

Thanks man, as always.