3.1

Solving 2-step equations

3.1 – Solving 2-step Equations

Goals / “I can…”Solve 2-step equationsUse deductive reasoning

3.1 – Solving 2-step Equations

When looking at an algebraic equation like

x + 7 = 15we try to figure out how to get x by itself. We

must get rid of the +7. To do this, we might say we undo the + 7 or do the opposite of + 7. Either way we could – 7 from both sides.

x + 7 = 15

-7 -7

x = 8

3.1 – Solving 2-step Equations

When looking at an algebraic equation like

½ x = 9we try to get x by itself. We must get

rid of the multiply by ½ by doing the inverse of that which is to multiply by the reciprocal or 2.

2(½ x) = (9)2 x = 18

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?

Recall the order of operations as you

answer these questions.

• Dividing by 2

• Subtracting 3

3 72

x

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 25. 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 = -3

+ 1 + 1

2x = -2

2 2

x = -1

2(-1) - 1 = -3

-2 – 1 = -3

1. Draw “the river”2. Add 1 to both

sides3. Simplify4. Divide both sides

by 25. Simplify6. Check your

answer

D U· 2- 1

+ 1÷ 2

+ 4 + 4

3 · · 3

x = 36

12 – 4 = 8

123

x

2) Solve 4 83

x

1. Draw “the river”2. Add 4 to both

sides3. Simplify4. Clear the fraction

-Multiply both sides by 3

5. Simplify6. Check your

answer

D U÷ 3- 4

+ 4· 3

364 8

3

3) Solve 3y – 1 = 8

7

3

1. y = 3

2. y = -3

3. y =

4. y = 7

3

Answer Now

3) Solve 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

63

d

1. d = -7

2. d = -19

3. d = -17

4. d = 17

Answer Now

5) Solve 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 = -35

2. z = -7

3. z = 35

4. z = 7

Answer Now

- 1 - 1

5 · · 5

3x = 15

3 3

x = 5

7) Solve 3

1 45

x

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

D U· 3 ÷ 5+ 1

- 1· 5÷ 3

33

5

x

3( )1 4

5

5

3.1 – Solving 2-step Equations

A music store sells a copycopy of a deluxe electric guitar for $295. This is $30 more than 1/3 the cost of the deluxe electric guitar it is modeled after. What is the cost of the deluxe guitar?