The following answer assumes that you are trying to solve a linear equation with one variable such as 31 = x + 4 + 2x
1) Combine any like terms that are on the same side. 31 = 3x + 4.
2) Use the Addition Property of Equality to "move" the variables to one side and the numbers to the other. In this case, add a -4 to both sides of the equation to get 31 -4 = 3x + 4 - 4 which yields 27 = 3x.
3) Use the Multiplication Property Of Equality to "separate" the variable from its coefficient. To do this, multiply both sides by the multiplicative inverse. In this case, multiply both sides by 1/3 to get 27(1/3) = 3x(1/3) which hields 9 = x.
4) Check Your Answer - Check the mathematical calculations that you completed to solve the equation. Put the answer back into the equation to see if "it works."
If your equation is part of a word problem, make sure that you have set up the word problem correctly. Also, make sure that your answer makes sense. If you are solving for something "real" such as bags of cookies, etc., make sure your answer is not a negative number.
If you have a system of equations:
1. Check to make sure in fact if the system is solvable. You will need as many unique equations as unknowns.
2. Determine which method would be most effective: substitution, elimination etc.
4. Plug back in values to the original equations to make sure there aren't any extraneous solutions.