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.
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.