Solving Equations with the Variable on Both Sides

Solving Equations with the Variable on Both Sides

by April Latham

​Just Remember...Don't Call Me After Midnight

• ​Distribute

• ​Combine like terms

• ​Move the variables to one side

• ​Add or Subtract to isolate the variable

• ​Multiply or Divide to isolate the variable

​Example 2

• ​Distribute: Distribute 7 to 2x and 5.

• ​Combine Like Terms: No like terms on the left or right side.

• ​Move the Variable: The variable is only on the left side, so no need to move one.

• ​Add or Subtract: Subtract 35 from both sides to isolate the variable.

• ​Multiply or Divide: Divide both sides by 14 to isolate the variable.

​Example 1

• ​Distribute: No parentheses, so nothing to distribute.

• ​Combine Like Terms: 10z and - 4z on the left; 8 and -15 on the right. You combine like terms on the SAME SIDE.

• ​Move the Variable: Add 2z to both sides (when you go from one side of an equation to another, you change the sign).

• ​Add or Subtract: Add 15 to both sides to isolate z.

• ​Multiply or Divide: Divide by 8 to isolate z.

​Example 3

• ​Distribute: Distribute the 2 to x and 5.

• ​Combine Like Terms: On the right side, combine 10 and -5.

• ​Move the Variable: Subtract 2x from both sides.

• ​Add or Subtract: Subtract 7 from both sides to isolate the variable.

• ​Multiply or Divide: Divide both sides by 3 isolate the variable.

​Example 4

• ​Distribute: Distribute the 5 on the right side to 4 and -6.

• ​Combine Like Terms: No like terms on the left or right side.

• ​Move the Variable: Subtract 5y from both sides.

• ​Add or Subtract: Subtract 2 from both sides to isolate y.

• ​Multiply or Divide: Divide both sides by -2 to isolate y.

Your Turn to Try a Few​

Multiple Choice

-3(4x - 7) = 93

• -8.333

• -6

• $$\frac{103}{4}$$  

• -9.5

Multiple Choice

9x + 4 = 7x + 16

• -6

• $$\frac{5}{4}$$  

• 10

• 6

Multiple Choice

2(3x - 1) = 7 + 5x - 4

• 5

• 13

• 4

• 12

Multiple Choice

𝟯𝙭−𝟭𝟬+𝟰𝙭=−𝟮(𝙭−𝟰)+𝟵

• $$\frac{27}{5}$$  

• 27

• 3

• $$\frac{11}{9}$$  

Multiple Choice

3(x + 1) = 5 + x

• 4

• 2

• 1

• -2

Fill in the Blanks

2(x + 1) = 18

Fill in the Blanks

4x + 13 = 2x + 23

Fill in the Blanks

2x = 20 - 2(x - 2)