Question regarding polynomial inequalities

Hi :) In my calculus class today, we had a lesson on solving polynomial inequalities. However, after my classmates and I got the answers to the homework wrong and I checked the internet, I suspect my teacher taught us wrong. Before I do anything about it though, I want to check for certain whether or not the method he gave us is wrong.

He told us to factor the polynomial, then treat each one as a separate linear function, and just bring it over across the sign (obviously flipping it if you multiply or divide by a negative).

For example, here's what he showed us to do for this question:

-x^2 + 4x - 4 > 0

-(x-2)^2 > 0

(x-2)^2 < 0

x-2 < 0

Two identical solutions: x < 2

However, I found the correct answer on the internet and in the text to be x = 2. This is just one of many where the answer I got using his method was wrong. Is what he did correct, or should it be done as these sites say:

Solving Polynomial Inequalities

Solving Polynomial Inequalities Analytically

Thanks so much to anyone who takes the time to read this and help :)

EDIT: It should read greater than or equal to.