How Do You Solve Equations With Variables on Both Sides?

To solve equations with variables on both sides, move the constants to the right side of the equation, simplify, move the variables to the left side and simplify. If the variable is negative, multiply both sides by -1 to make it positive.

While an equation with variables on both sides can look intimidating, the steps to solve it are quite easy. Use the equation 5y-3=3y+5 as an example.

1. Move the constants to the right
2. Move the constants to the right by subtracting or adding to both sides. In the example equation, this step would be 5y-3+3=3y+5+3. Each side has to be treated the same. Then simplify to 5y=3y+8.
3. Move the variables to the left
4. Move the variables to the left of the equation by subtracting or adding to both sides. Using the example equation, this step would be 5y-3y=3y-3y+8. Remember to do the same thing on both sides. This step simplifies down to 2y=8.
5. Reduce the variable
6. If the variable has a number in front of it, as when moving the variables to the left, it need to be reduced down to a single variable. To do this, just use simple division. With an answer of 2y=8, the variable needs to be divided by 2 in order to be a single variable. This means the constant on the right needs to be divided by two also. Therefore, y=8/2 or, simplified, y=4.
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