solve two-step equations using inverse operations

ObjectiveThe student will be able to:

Designed by Skip Tyler, Varina High School

Two-step Equations

To solve two-step equations, undo the operations by working backwards.

Example:

Ask yourself, 1. What is the first

thing we are doing to x?

2. What is the second thing?

3 72

x Recall the order of

operations as you answer these questions.

• Dividing by 2

• Subtracting 3

To undo these steps, do the opposite operations in opposite order.

1. Draw “the river”2. Add 3 to both sides3. Simplify4. Clear the fraction -

Multiply both sides by 2

5. Simplify6. Check your answer

Use a DO-UNDO chart as a shortcut to answering the questions. In the table, write the opposite operations in the opposite order

DO UNDO ÷2 -3

Follow the steps in the ‘undo’ column to isolate the variable.

3 72

x

+ 3 + 3

= - 4

x = -8

-4 – 3 = -7

2

x

+3

· 22 · · 2

38

72

1) Solve 2x - 1 = -31. Draw “the

river”2. Add 1 to both

sides3. Simplify4. Divide both

sides by 25. Simplify6. Check your

answer

+ 1 + 1

2x = -2

2 2

x = -1

2(-1) - 1 = -3

-2 – 1 = -3

D U· 2- 1

+ 1÷ 2

+ 4 + 4

3 · · 3

x = 36

12 – 4 = 8

123

x

2) Solve

1. Draw “the river”2. Add 4 to both

sides3. Simplify4. Clear the

fraction -Multiply both sides by 3

5. Simplify6. Check your

answer

4 83

x

D U÷ 3- 4

+ 4· 3

364 8

3

3) Solve 3y – 1 = 8 1. y = 32. y = -3

3. y = 4. y =

7

37

3

Answer Now

d 4

23

d – 4 = 6

+ 4 + 4

d = 10

1. Draw “the river”2. Clear the fraction -

Multiply both sides by 2

3. Simplify4. Add 4 to both

sides5. Simplify6. Check your

answer

D U- 4÷ 2

· 2+ 4

42 3 2

2

d

10 43

2

4) Solve1. d = -72. d = -193. d = -174. d = 17

16

3

d

Answer Now

3 27

a

-3 -3

a = 35

1. Draw “the river”2. Subtract 3 from

both sides3. Simplify4. Clear the fraction

– Multiply both sides by -7

5. Simplify6. Check your

answer

D U÷ -7+ 3

- 3· -7

Do/Undo Chart – This one is tricky! Remember to always use the sign in front of the number.

57

a

7 5 77

a

3 235

7

3 5 2

6) Solve 5z + 16 = 51 1. z = -352. z = -73. z = 354. z = 7

Answer Now

- 1 - 1

5 · · 5

3x = 15

3 3

x = 5

7) Solve

1. Draw “the river”2. Subtract 1 from both

sides3. Simplify4. Clear the fraction -

Multiply both sides by 5

5. Simplify6. Divide both sides by

37. Simplify8. Check your answer

31 4

5

x

D U· 3 ÷ 5+ 1

- 1· 5÷ 3

33

5

x

3( )1 4

5

5