8th Grade - Multi-Step Multi-variable Equations


  • You have already learned how to solve simple equations like x-2=5. These can be solved in one step.
  • The equations like 7x-3=18 or 2x+3=3x-3 would need more than one step to solve.

Solving Two Step Equations

  • The two-step equations can be solved using inverse operations.

Solving Multi Step Multi Variable Equations

  • If there is a parenthesis, use the distributive property to get rid of it.
  • Combine all like terms after using the distributive property.
  • Use inverse operations to isolate the variables, if needed.
  • Finally, eliminate the constant or variable term from one side of the equation.

Solved Examples

  • Solve 2x-10=30

Add 10 to both sides (addition property of equality).



Divide both sides by 2 (division property of equality).



  • Solve 4x+2=20

Use the distributive property.


Subtract 8 from both sides (subtraction property of equality).



Divide both sides by 4 (division property of equality).



Cheat Sheet

  • Get rid of the parenthesis first, if any.
  • If you have to perform any operation like adding a term, subtracting a term, multiplying, or dividing, perform the same operation on the other side.

Blunder Area

  • Whatever you do to one side of the equation, do the same to the other side of the question.
  • Pay close attention to the signs while using the distributive property.
  • Pay close attention to the signs while doing inverse operations.