x ≥ y is it inequality?

It might be equal or it might not. So it is not an equality. So it is an inequality.

It's called an "inequality" because the full solution set includes instances where x and y are not equal.

The mathematical use of a word does not always match everyone's ordinary English use of the same word, which is a good reason to pay careful attention to definitions.

The only relation that completely matches the English meaning of "inequality" is the ≠, and f(x) ≠ g(x) is an inequality. It's usually not studied because (a) the solution set usually isn't of interest, and (b) the solution method is exactly the same as solving the equation f(x) = g(x). The solution set of one is simply the complement of the other.

x ≥ y

https://www.wolframalpha.com/input/?i=x+%E2%89%A5+y

An inequality has <, >, ≤ or ≥.
An equality has =

Unless you see just the equal sign (=) it is an inequality.

Just because one of the possible cases is that the two values are equal, you can still have a case where the values are not equal. So it is an inequality.

It's a good question and I can see where the confusion comes in.

Perhaps if you think in English words, it will make this clearer.

Let's say Xavier has x jellybeans
And let's say Yolanda has y jellybeans.

If I say Xavier has at least as many jellybeans as Yolanda, I would write:
x ≥ y

But even if I know how many Yolanda has, I still don't know exactly how many Xavier has. He might have the same, or he might have more.

Only an equality would tell me how many Xavier has relative to Yolanda.

its an inequality b/c it is greater or equal. There is a possibility that it could be unequal, which makes it an unequality

y ≤ x_______is indeed an inequation

Draw the line y = x then shade the region below that line.
This region represents y ≤ x