[javajosh]

The term is not meaninglessly broad here in the US. We use the term "abstract algebra" to describe the more general subject, usually taught in college-level courses in groups, fields, and so on. Mere 'algebra' does indeed mostly mean "solving for an unknown", although I'd argue there's an important, more general concept of 'equation' introduced. From what I've read the concept of 'variable' is tricky for a lot of kids.