From the another thread:

Do you guys know if anyone has written down rules for solving equations with variables? Here’s what I’m getting at: When you solve an equation with a variable, the sequence of actions you will take to isolate a variable. It seems like the first action you choose can be crucial, too. For example, look at this equation:

7(2e−1)−11=6+6e

What should you do first? I saw this at Khan Academy, and they used the distributive property first–getting “rid of” the 7 outside of the parenthesis. That does seem like the best move, but I didn’t realize that initially. I think I might have tried to add 11 to both sides first. And then my instinct might have been to divide by 7 on both sides, but I think that would have been a mistake. In working on several of these type of problems prior to this one, one of the important early moves involved “getting rid of” the number being multiplied by an operation with a parenthesis. For example,

200 = 20(4c+2)

I guess you could use the distributive property first, too.

In any event, I’m trying to find a list of rules or principles that will guide a student on the sequence of operations they should choose. What should be the first step, and then the second, third, etc. I did a quick search for something like this, but didn’t see anything.