Variables on Both Sides

You are familiar with the first type of equation in the table below. The variable is on one side of the equal sign, and there is a constant (number) on the other side. To solve, you simply divide both sides by two.

In the second equation, each side has both a variable and a constant. The variable on each side of the equation has the same value. In this example, the variable on the left side of the equation represents the same number of cookies as the variable on the right side of the equation. Let x = one box of cookies. Two boxes of cookies are equal to four cookies. 2x = 4 Let x = one box of cookies. Two boxes of cookies plus one extra cookie are equal to one box of cookies plus three extra cookies. 2x + 1 = x + 3

To solve equations with variables on both sides, you will follow the same steps that you have applied to previous equations. You can use the following equation to review each of these steps.

 Solve the Equation: 12x – 5 – 2x = 24x – 33 1 Combine like terms on each side of the equation. 10x – 5 = 24x – 33 2 Move the variables to one side of the equation by using inverse operations and combining like terms. 10x – 10x – 5 = 24x – 10x – 33 –5 = 14x – 33 3 Move the constants to the other side of the equation by using inverse operations and combining like terms. – 5 + 33 = 14x – 33 + 33  28 = 14x 4 Isolate the variable by using inverse operations. 2 = x Tip: You can move the variables to either side of the equation. It may be easier to move the variable so that it ends up with a positive coefficient.                                                  2 x – 5 = 7 x – 10  Now try solving the following equation on your own: 8x – 4 = 2x – 16.

Click on the Show Answer button below to check your answer. Answer:
8x – 4 = 2x – 16
8x – 2x – 4 = 2x – 2x –16
8x – 2x – 4 = –16
6x – 4 = –16
6x – 4 + 4 =  –16 + 4
6x = –12
x = –2

Click on the link below to watch the "Solving Equations with Variables on Both Sides" Teachlet® tutorial. Watch the tutorial up to the time 3:20. Solving Equations with Variables on Both Sides