Thank you for explaining. Hard to believe that 13 year olds could fail to do this, or at least formally manipulate the equation till they have a satisfactory answer. Something is wrong with pedagogy or the process of practice.
What's wrong with the pedagogy is the idea that no one should be taught any material until everybody is capable of learning that material. Variable manipulation can be easily learned by 4th graders. But it can't be learned by all 4th graders, so everyone has to wait.
Just in case you think I might be misleading you somehow, here's a cheat sheet product for a "college algebra" course; again, "college algebra" refers to the material that would normally be covered in or before high school, except that it's being covered in college. So the idea of this product is that current college students will buy it to help them understand what's going on in class, or to review for a test.
Many 4th graders would have genuine trouble grokking the notion that a variable (a "letter") may be used in an expression to stand for some arbitrary number. This is why it may be more sensible to reinforce quasi-algebraic reasoning at that age by indirect means, such as practice with non-trivial word problems and with e.g. computing expressions that involve a variety of operations w/ rules of precedence, parentheses etc.
