x^2 - x < 0.
Why is this equal to 0<x<1?
When we take x as common:
x (x-1) < 0
Why is not x < 0 then?
the answer is simple
u have already done the factorization : x (x-1) < 0
now assume that there is an '=' sign and get the values of x
u get two values : x=0 and x=1
Plot these on a number line and divide the number line on the inflection points
Number line will be divided into 3 parts
label the parts alternately as + ,-,+ (this can go on if u have more regions)
-- ensure that you start labelling from the right side and always start with a + and keep on alternating
as the inequality sign is negative .. u will choose the - region which is 0<x<1
If the inequality sign was positive
u would have chosen the 2 positive parts..
Hope this helps