aazhar wrote:

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