I find that my algebra students feel daunted by a really long algebraic equation they need to solve. I encourage them to treat it like cleaning and organizing.
How to simplify and solve an algebraic problem:
1. Are there parentheses? Get rid of them! Complete all possible operations within the parentheses. (Multiply out if there is a multiplier outside of the parentheses).
2. Are there exponents on regular numbers? Yuk! Get rid of them! Perform the exponent operation. If there are exponents on variables, just leave them alone for now.
3. Make all mixed numbers improper fractions and find common denominators OR use least common multiple method to make them whole numbers.
4. Combine all like terms on both sides of the "=" (Think of them like last names. Such as: 2a+10a becomes 12a, XY-3xy becomes-2xy, -50+15 becomes -35. You CANNOT group 3a + 2ab because they do not actually have the same last name!)
5. Decide which side of the "=" you want the regular numbers, and which side you want the variables.
6. Using inverse operations, start with the regular numbers (the ones without a variable) to get them all on one side of the "=". Tidy up!
7. Then get all the variables to the other side of the "=" also through inverse operations. Even tidier!
8. See if anything can be grouped again. It's getting cleaner!
9. Continue using inverse operations to get the single variable on one side of the "=", and a number on the other side to solve. Presto! Even Mr. Clean is jealous.