Does the order of operations matter with just addition and subtraction? Had a debate on whether you could do addition/subtraction in any order you want. Specifically, for the following:
$9 - 4 + 3$
We both agree that the answer is 8.
I argue that, by giving addition a higher priority than subtraction (rather than the same priority and going left-to-right), you would end up with $9 - 4 + 3 = 9 - 7 = 2$, which is an incorrect answer, and therefore it matters that addition and subtraction have the same priority.
The other person argues that the order of operations doesn't matter and that it can be done in any order, as by giving addition a higher priority than subtraction, you would end up with $9 - 4 + 3 = 9 + (-4 + 3) = 9 + - 1 = 8$, which is the correct answer, and therefore it wouldn't matter if addition/subtraction had different priorities rather than the same.
I'm arguing that bringing the $- 4$ inside the bracket and then performing it before the $+ 3$ wouldn't be done if addition had a higher priority. The  fairly long, debate can be seen here if you want to read it, so I don't paraphrase it all and bias my side too much.
My overall question is who is correct; does the order of operations matter with just addition and subtraction? I'm willing to accept answers for either side, so long as they give a reason.

It does matter because it reflects the convention of which procedures are first performed to evaluate a given mathematical expression.
