Solve the inequality x^3+4x>5x^2.
Divide by x: x^2 + 4 > 5x
Move terms: x^2 - 5x + 4 > 0
Factor: (x - 1)(x - 4) > 0
Answer: (-inf,1) U (4,inf)
Here is another way to put it:
We find the GCF of all of the terms, which is x. That will get us x^2+4>5x
This can be set into a quadratic (ax^2+bx+c).
In this case, the quadratic will be x^2-5x+4.
We will then factor the quadratic, which will get us (x - 1)(x - 4) > 0
The possible values of x will be x=1 and x=4.
If we write this in interval notation, it will be (-infinity, 1) U (4, infinity)