This inequality can be rewritten as:

x^2 - 11x + 10 >= 0

Next, we need to factorize the quadratic expression:

(x - 10)(x - 1) >= 0

Now we can determine the critical points by setting the expression equal to zero:

x - 10 = 0 => x = 10
x - 1 = 0 => x = 1

Now we can determine the sign of the expression in each of the intervals created by the critical points:

For x < 1, both factors are negative, so the expression is positive.
For 1 < x < 10, one factor is negative and one is positive, so the expression is negative.
For x > 10, both factors are positive, so the expression is positive.

Therefore, the solution to the inequality x^2 - 11x + 10 >= 0 is x <= 1 or x >= 10.