Algebra I Recipe: Solving an Equation with Variables on Both Sides (Multi-Step Equations)

1. Change subtraction to “adding the opposite” when necessary.



2. Do the distributive property on each side.



3. Combine like terms on each side.



4. Get the variable terms on the same side of the equation.
   • Add or subtract the one variable term to get it to the side of the variable term with the larger coefficient.



5. Move the number term by adding or subtracting.
   • Add if the number term is negative.
   • Subtract if the number term is positive.



6. Move the coefficient by multiplying or dividing.
   • If the coefficient is a fraction, multiply by its reciprocal on both sides.



7. If the variable terms cancel on both sides.
   • The answer is no solution if the variable terms cancel and a false statement remains.
   • The answer is all real numbers if the variable terms cancel and a true statement remains.