You're right, my mistake. That "five higher" should have been "four higher".
The thing is that your solution is the algebraic solution. You're simplifying an equation by balancing both sides, when you subtract four. Just from our perspective, you simplify to a still difficult state, instead of the easiest possible state.
Algebra is just a way of formally stating what you did, and then offering some simplifications that speed up the process. Or offering more powerful methods that making solving more difficult problems easier.
'The thing is that your solution is the algebraic solution'
I agree. That's why I said
'Really, the trick mention(ed) ... is just a rephrasing of the algebra'
Just because you do number juggling in your head rather than write it formulaically doesn't make it an inferior technique, or make it not algebra, which was my point.
The thing is that your solution is the algebraic solution. You're simplifying an equation by balancing both sides, when you subtract four. Just from our perspective, you simplify to a still difficult state, instead of the easiest possible state.
Algebra is just a way of formally stating what you did, and then offering some simplifications that speed up the process. Or offering more powerful methods that making solving more difficult problems easier.