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.