# Solving an equation with a variable on both sides

Solving an equation with a variable on both sides of the equation require a few more steps. However, it is not complicated at all once you understand how to solve two-step equations.

Example #1

Solve 9x - 12 = 5x + 8

9x - 12 = 5x + 8

Subtract 5x from each side of the equation

9x - 5x - 12 = 5x - 5x + 8

4x - 12 = 0 + 8

4x - 12 = 8

Add 12 to each side of the equation

4x - 12 + 12 = 8 + 12

4x + 0 = 20

4x = 20

Divide each side by 4

4x/4 = 20/4

x = 5

Check

9x - 12 = 5x + 8

9(5) - 12 = 5(5) + 8

45 - 12 = 25 + 8

33 = 33

Example #2

Solve 3y + 11 = 31 - 7y

3y + 11 = 31 - 7y

Add 7y to each side of the equation

3y + 7y + 11 = 31 - 7y + 7y

10y + 11 = 31 - 0

10y + 11 = 31

Subtract 11 from each side of the equation

10y + 11 - 11 = 31 - 11

10y + 0 = 20

10y = 20

Divide each side by 10

10y/10 = 20/10

y = 2

Check

3y + 11 = 31 - 7y

3(2) + 11 = 31 - 7(2)

6 + 11 = 31 - 14

17 = 17

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