I think of what you were talking about is a linear equation with one variable. Well, it's just simple and easy. Just derive the equation, use different properties. How can you say/How would you know what property to use? Just simple, know the inverse property used. Just for example we have this equation:

5x + 9 = 19
5x + 9 - 9  = 19 - 9 (Addition to Subtraction)
5x/5 = 10/5 (Multiplication to Division)
x = 2

Hope you understand my explanation.