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» » Equations with Variables on Both Sides

Solving Algebra Equations with Variables on Both Sides

Solving algebra equations with variables on both sides is really tough. But, you will have no problems solving these equations after you follow the step-by-step instructions in these 3 examples.



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!


Solving algebra 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.

  • 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


equations with variables on both sides




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



Example 2


algebra equations

Yes, this is a confusing topic, so if you are still having trouble, check out example 2 on video.

youtube channel If you want to see this example on video, click here to visit my You Tube channel.

If you are still having trouble, check out the Pre-Algebra Refresher Course which includes 12 lessons on Solving Equations! It's Free, just click here.

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


Example 3


equations with variables on both sides

Example 3 on video...

youtube channel If you want to see this example on video, click here to visit my You Tube channel.

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!





Take a look at the questions that other students have submitted on equations with variables on both sides:

question and answers

Variables on Both Sides: 4p +40 = 26p


Variables on Both Sides (with Fractions): 3/7w - 11 = -4/7w


Variables on Both Sides (and the distributive property): -11-5a = 6(5a+4)


Variables on Both Sides: 2c+6 = 1-3c


Another Variables on Both Sides: 4x - 5 = 12x -69

To ask a question, please visit my Math Forum.



Other Lessons You Might Like on Solving Equations


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