No, the problem here is that the word ALGEBRA has two meanings, in high school vs college+ contexts. They share the same name and in both you can state that ax

No, the problem here is that the word ALGEBRA has two meanings, in high school vs college+ contexts. They share the same name and in both you can state that ax=bx => a=b ... but the similarities end soon after. The material here is precisely what you'd expect in your first (i.e., basic) college algebra class.