3(x^2 - 7x) < 0
divide both sides by 3
x^2 - 7x <0
factor
(x)(x - 7) < 0
consider all possible cases. in order for the product of two quantities to be negative, one must be negative and the other must be positive
case 1:
x < 0 but x - 7 is not < 0
this case is impossible (if x is negative, then x - 7 is also negative)
case 2:
x - 7 < 0 but x is not < 0
x must be less than 7 but greater than 0
therefore 0 < x < 7
