Would This Be Correct?

Yes
Exactly.
Yes, good job!
It is, nice work!
Yes it is correct, however.

WHY do you think it is? What reasoning are you using to conjecture that that general case is always true? And the reason I ask is actually a VERY common problem that comes up among math learners, and that is believing that a pattern that they find is true.....pretty much just because. Don't get me wrong; math is all about recognizing patterns and formalizing them, and in that I think you have succeeded. But that's not enough; once you have what you think is a pattern, you want to be able to say WHY it's a pattern, and how you KNOW it always holds, or if it doesn't always hold, WHEN it holds.

In this case, it's real easy: you can multiply X on the Left Hand Side by 10/10 (since 10/10 = 1), note the common denominator, and add. And for something as simple as this, that sure feels like a hoop I'm just trying to make you jump through. But when the patterns get more complex and subtle, it'll get harder, but also more necessary, because your everyday intuitive pattern-matching won't cut it anymore.
yes, thats how fractions work
Yeah, X = 2X/2 = 3X/3 = 10X/10 etc
I love that you used an example to help convince yourself that it's correct. Well done!