Binomial coefficients inequation problem Can anyone help me solve this:
$$5\binom{13}{x} < \binom{x + 2}{4}$$
After turning it to factorial I don't know what to do nothing seems to cancel out. $x$ is a positive integer.
I end up with this when trying to solve it:
$$\frac{13!}{x(x+1)(13 - x)!} < \frac{(x+2)!}{5!}$$
Edit: I found solutions in a book with this task, says solutions are {11, 12, 13} I've plugged them in and they seem to work. But can anyone explain how it was solved?

$x>10$.  I got this simply by plugging in all the values of x from 2 to 13.
Here is the Mathematica code and output I wrote:
Do[Print[5*13!/(x!*(13 - x)!) - (x + 2)!/(4!*(x + 2 - 4)!)], {x, 2, 13}]

389
1425
3560
6400
8510
8454
6225
3245
935
-325
-936
-1360

