Why add before dividing in this equation? For the following equation, I know the correct answer is $9$:
$$
x / 3 + 2 = 5
$$
You subtract $2$ from each side, and the multiply each side by $3$...
But why do you subtract the $2$ first?
Doesn't the order of operations say I should do division before addition?

As regards correctness of the solution, the order is irrelevant as long as the operations are legal.
$$\frac x3+2=5.$$
First times $3$:
$$x+3\cdot2=3\cdot5,\\x+6=15,$$
followed by minus $6$:
$$x=15-6,\\x=9.$$
Or first minus $2$:
$$\frac x3=5-2,\\\frac x3=3,$$
followed by times $3$:
$$x=3\cdot3,\\x=9.$$
It's a matter of taste, except that in the first case you perform two multiplies and one subtract, vs. one subtract and one multiply in the second.
