Find the Minimum Value of k

Question
We are given 2014 positive numbers such that

x(1) < x(2) < x(3) <… < x(2014)

It is known that the number x(k) is 19 times the average of the 2014 numbers.

Determine the “minimum” possible value of k

A Possible Solution

(Please refer to the attached image)

I think the answer is
K (min) = 1910