Variables on both sides

Solve Equations

with Variables

on Both Sides

When you see an equation with variables on both sides you should:

• Move all the terms with variables to one side of the equation by making the term zero on one side.

• Remember that terms with variables can become zero the same way constants become zero: by adding the opposite or using the inverse operation.

• The equation stays balanced when you do the same thing to both sides.

It looks like this:

It could look like this:

Multiple Choice

Let's try it! Choose the correct first step for this equation.

$$\ 7x\ =\ 2x\ -\ 20$$  

• Subtract 2x from both sides.

• Subtract 7x from both sides.

• Sutbract 20 from 2x.

Is this what you said?

Multiple Choice

Using the work we just did, find the solution for

$$\ 7x\ =\ 2x\ -\ 20$$  

• x = 4

• x = -4

• x = 15

• x = -25

Multiple Choice

Try another one. Choose a correct first step for this equation.

$$14\ +\ 3n\ =\ 5n\ -\ 6$$  

• Subtract 5n from both sides.

• Add 14 to 3n

• Subtract 6 from 5n

Is this what you thought?

Here's another option:

Multiple Choice

Using the math we just saw, solve this equation.

$$\ 14\ +\ 3n\ =\ 5n\ -\ 6$$  

• n = 10

• n = -10

• n = -18

• n = -22

Multiple Choice

Let's practice some more. What is the solution to this equation?

$$18\ -\ 2g\ =\ 4g$$  

• 3 = g

• g = 12

• 9 = g

• g = 16

Multiple Choice

Try one more:

$$3x\ +\ 5\ =\ 7x\ +\ 4$$  

• $$x\ =\ 4$$  

• $$x\ =\ -4$$  

• $$x\ =\ \frac{1}{4}$$  

• $$x\ =\ -\frac{1}{4}$$  

Multiple Choice

7w + 5 = 3w - 15

• w = 5

• w = -2

• w = 2

• w = -5

Multiple Choice

Solve for x:
5x - 14 = 8x + 4

• x = 6
• x = -6
• x = -18/13
• x = 10/3

Multiple Choice

-5k + 10 = -2k - 14

• k = 8

• k = -8

• k = 2

• k = -2

Multiple Choice

10x + 9 = 4x - 9

• x = 0

• x = 3

• x = -3

• x = -18

Multiple Choice

8x - 8 = -4x + 16

• x = 8

• x = 16

• x = 24

• x = 2

Multiple Choice

7w + 5 = 3w - 15

• w = 5

• w = -2

• w = 2

• w = -5

Multiple Choice

Solve: -2x + 18 = 2x + 40

• x = -5.5

• x = 6.5

• x = -4.5

• x = 5.5

Multiple Choice

Solve: 4x - 3 = 6x - 19

• x = -8

• x = 11

• x = -11

• x = 8