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Basic Algebra

Basic Algebra

Solving Equations with Variables on Both Sides

If you encounter a variable on both sides of the equal sign, don't assume it's a typo and move on to the next problem; it may very well be there on purpose. The key to solving these types of equations is to move all the terms containing the variable to one, and only one, side. It doesn't matter which side you choose, just try to pick the easier one.

As before, there are a lot of different ways to solve these problems. Choose whatever way floats your boat.

2x - 6 = 5x + 18

Method #1: Get all the variables on the right-hand side.

2x - 6 = 5x + 18
2x - 6 - 2x = 5x + 18 - 2xsubtract 2x from each side
-6 = 3x + 18combine the like terms
-6 - 18 = 3x + 18 - 18subtract 18 from each side
-24 = 3xsimplify
-24/3 = 3x/3divide each side by 3
-8 = xand done!

Method #2: Get all the variables on the left-hand side.

2x - 6 = 5x + 18
2x - 6 - 5x = 5x + 18 - 5xsubtract 5x from each side
-3x - 6 = 18combine the like terms
-3x -6 + 6 = 18 + 6add 6 to each side
-3x = 24simplify
-3x/-3 = 24/-3divide each side by -3
x = -8same answer

Don't forget to check:

2(-8) - 6 = 5(-8) + 18

 -16 - 6 = -40 + 18

-22 = -22

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