Solving Equations with Variables on Both SidesSolving Equations with Variables on Both Sides

Steps to Solve Equations with Variables on Both Sides

(1) Take care of any parenthesis by distributing.

(2) Combine all like terms on each side of the equal sign.

★ Same Side, Same Operation

(3) Get variables to one side of =. Moving the smallest will avoid dividing by a negative.

★ Opposite Side, Opposite Operation

(4) Isolate term with variable.

★ Opposite Side, Opposite Operation

• Multiply or Divide to get coefficient of variable to 1.

Solve:✦ Variables together

Opposite side = Opposite operation

✦ Moving the smallest avoids dividing by a negative.

✦ Isolate variable term.

✦ Divide by variables coefficient to make coefficient of variable 1.

2a 3 5a 8

3 3a 8

2a 2a

8 8

5 3a 3 3 5

3a

Solve:✦ Distribute.

✦ Variables together, moving smallest. Opposite side = Opposite operation

✦ Isolate variable term.

✦ Divide to make coefficient of variable 1.

3 x 2 7 x 5

4x 6 35

7x 7x

6 64x 41 4 4

x 41

4

3x 6 7x 35

Solve:✦ Distribute.

✦ Combine like terms on left side.

✦ Variables together, moving smallest. Opposite side = Opposite operation

✦ Isolate variable term.

✦ Divide to make coefficient of variable 1.

9 2x 3 5 x 3

19x 22 31x 1x

22 22

19x 19 19 19

x 1

18x 27 5 x 318x 22 x 3