Solving Algebra Equations with Variables on Both Sides



equations with variables on both sides



This is it! Our last type of equation to solve before applying our knowledge to solve real world problems! Yes... the whole reason we are learning to solve these equations!



So far, you've learned how to solve one-step equations, two-step equations, and equations with fractions. If you haven't mastered these skills or need a refresher, please go back and review these lessons before attempting this one! It will be so much easier if you have the background!

So, if you are ready, let's move on!


Equations with variables on both sides look intimidating, but they really aren't that hard if you have the background skills. In fact, I think these types of equations are fun because it's like moving pieces of a puzzle around.

This is what you need to remember:

  • If you have any fractions, get rid of those first by multiplying ALL terms by the denominator.

  • Use the distributive property if needed.

  • Your ultimate goal is to get all of the constants on one side of the equation and all of the variables on the other side of the equation. You can accomplish this by adding or subtracting terms on BOTH sides of the equation.


    		•

    Let's look at a few examples.



    Example 1

    variables on both sides



    Need Help With Your Own Problems?

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    This next example shows how to solve if the distributive property is involved.



    Example 2

    variables on both sides



    This last example shows how to solve if fractions are involved.


    Example 3

    variables on both sides



    It doesn't look too hard, does it? Remember: it's like moving puzzle pieces around - all the variable terms on one side and all the constant terms on the other side!

    Here's a few practice problems for you to try!



    algebra equations with variables on both sides


    Variables on Both Sides Practice Problems

    solving algebra problems









    Answer Key for Variables on Both Sides

    solving algebra problems answers


    If you want online, interactive practice with balancing and solving algebra equations with variables on both sides, click here to play an Algebra game.

    Otherwise, I think you are ready to move onto Solving Algebra Equations within Word Problems!


    Solving Equations Unit

  • Balancing Equations

  • Solving one-step equations (Addition).

  • Solving one-step equations (Subtraction).

  • Solving one-step equations (Multiplication).

  • Solving one-step division equations.

  • Solving two-step equations.

  • Solving Equations with the Distributive Property

  • Solving equations with fractions

  • Solving Literal Equations

  • Solving algebra equations with variables on both sides You Are Here!

  • Writing equations given a word problem The Next Lesson!



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