Question

How does one solve a question which is a binomial not a trinomial? The answer is 0<x<7

Answer 1

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