Most grammarians and teachers agree that “alright" is informal, which basically means that you shouldn’t use it in essays for school.
However, so many people are—and have been—using “alright” that it might soon be “all right” to use “alright” in essays. But until then, avoid “alright” at all costs in formal writing.
It is understandable that many people use “alright” (and assume that it’s correct); after all, other common words that begin with “al-" are considered standard:
In closing, even though “all right” is better than “alright,” you should consider using “adequate,” “satisfactory,” or some other synonym to make your writing sound a bit more sophisticated. After all, “all right” is only all right; it’s not great.