x^2-3x-4>0 is an example of an inequality. (x-4)(x+1)>0; for this to be true the two factors must be both positive or both negative.

Both positive: x-4>0, x>4; x+1>0, x>-1. So x must be greater than 4 because 4>-1.

Both negative: x-4<0, x<4; x+1<0, x<-1. So x must be less than -1 because -1<4.

**The solution is that x<-1 or x>4**.

Substitute x=0. This value is not expected to satisfy the inequality. With x=0 we have -4>0, which is false, as expected.

Substitute x=-2: we have 4+6-4>0. True.

Substitute x=5: we have 25-15-4>0. True.

x=-1 expected to be false. We have 1+3-4=0. False because 0 is not greater than 0.