Solve the inequality: x^2 - 3x < 0 . How is the answer 0 < x < 3?

Answer 1

x^2<3x if x cannot be zero, then
x<3
now if x had been negative, the equality x^2<3x when divideing by x would have been x>3, but that is not possible for a negative number to be >3, so 0<x<3

Answer 2

x (x-3) is supposed to be negative
if x >3 it is positive
if x <0 it is positive

it is only positive * negative = negative between 0 and 3