It's terribly context-dependent - in my native context "algebra" starts with group theory, but that's not a context relevant to you... As I understand it "algebra" in a US high school context starts with "Algebra 1" which follows on from a thing called "pre-algebra" which is not itself considered to be algebra (although what the qualitative difference is, do not ask me :-)
Art of Problem solving has useful pre- and post-tests for its courses, which include Algebra 1. Here are a couple of questions from their *pre*-test for Algebra 1 - that is, these are questions you are supposed to be able to do before you are ready to begin what the US calls algebra (they themselves count as "pre-algebra").
2. Solving linear equations.
(a) Find x: 31x + 24 = 365.
(b) Find n: 7n - 4 = 2n + 16.
(c) Find y: 3(10 + y) = 81.
3. Working with variables.
(a) Expand the product 9(3x + 7).
(b) Simplify: 7a - 5b + 3(6a + b).
(c) Simplify: a - (-7a - 3).
At any rate, these are basic enough that I think it's fair to say that if Junior *cannot* do these easily, you should *not* be saying that Junior can do algebra. Really I'd suggest that it's probably not useful ever to say "Junior can do algebra" - much better to say specifically what Junior can do, either by specific skills or by reference to a particular syllabus.
