Warm-up:Solve each equation & check your answer.

1) 2)

34x 5

29

w 3

43

43

x 5143

x 203

623

✔

34203

5

29

29

w 329

✔

29

329

3

Warm-up Continued…

What is the LCD of the following fractions?3) 4)

5)

18,

12,

34

LCD : 8

15,

14,

310

LCD : 20

116,

18,

332

LCD : 32

Solving Two-Step Equations:Algebra Tiles,

Friendship Analogy,& MOREInteractive

Algebra

Creating an Equation & then Undoing It

Creating an Equation: Undoing to Solve:

x 3

2x 6

2x 5 11

2x 5 11(2) (2)5 + + 5 – 5 – 5

2x 62 2

x 3

Equivalent Equations

Show on the whiteboard.

_______________________________________________________________

Equivalent equations have the same solutions.

x 6All of these

have the SAMESOLUTION:

x = 6

Two step equations with algebra tiles:• No need to draw or write these. Just demonstrate with algebra

tiles:

Equation:

2x 1 7

Create ZERO pairs

0 =

x 3

Two step equations with algebra tiles:• No need to draw or write these. Just demonstrate with algebra

tiles:

Equation:

4 3x 2

Create ZERO pairs

x 2

Two step equations with algebra tiles:• No need to draw or write these. Just demonstrate with algebra

tiles:

Equation:

5 3 2x

1 x

x 1

Two-Step Equation Friendship Comparison

9y 5 8Best friend (coefficient)

Just a friend(constant)

You Otherside of

the scale(outside the

party)

3w4

7

Two-Step Equation Friendship Comparison

Best friend(coefficient = ¼)

Just a friend(constant)

YouOtherside of

the scale(outside the

party)

EXAMPLE 1: Solving Two-Step Equations

• Solve each equation.1A) ✓ for balance:

18 4n 10– 10– 10

8 4n44

2 n

n 2

18 4n 10

18 4(2)10

18 810

18 18 ✓

EXAMPLE 1: Solving Two-Step Equations

• Solve each equation.1B) ✓ for balance:

32 2 5x–2–2

30 5x–5–5

x 6

32 2 5x

32 2 5( 6)

32 2 30

32 32 ✓

1C) ✓ for balance:

EXAMPLE 2: Solving Two-Step Equations that Contain Fractions

11m4

20+11+11

m4

9(4) (4)

m 36

11m4

20

11 364

20

11 9 20

20 20✓

EXAMPLE 2: Solving Two-Step Equations that Contain Fractions

• Solve each equation. Method 1:

____________________________

y8

34

54

Multiply by the LCD: CLEAR the fractions.

( )8 ( )8

81

y8

81

34

5481

2 2

y

6

10+6 +6

y 16

EXAMPLE 2: Solving Two-Step Equations that Contain Fractions

• Solve each equation. Method 2:

____________________________

y8

34

54

Use fraction operations

34

34

y8

84

81

81

2

y 16

Circle or * the method you

like the best.

✓ for balance:

y8

34

54

168

34

54

84

34

54

54

54

✓

168

÷2÷2

2A)

Which method should we use?

23w

34

712

EXAMPLE 2: Solving Two-Step Equations that Contain Fractions

✓ for balance:

What LCD should we use for Method #1?

(12)(12) (12)

8w 9 7

23w

34

712

34

912

23w

212

32

32

w 14

8w 2

w 28

14

23

14

34

712

212

34

712

212

912

712

✓

4 3 1–9 –9

8

1

4

2B)________________

Which method should we use?

1315n

83

EXAMPLE 2: Solving Two-Step Equations that Contain Fractions

✓ for balance:

What LCD should we use for Method #1?

(15) (15) (15)

5 3n 40

1315n

83

13

13

15n

93

51

51

n 3(5) 15

3n 45

n 15

1315151

83

13 3

83

223

83

✓

–5 3 5+5 +5

3 3

Practice:

• Solve each equation.1)_____________________ ✓ for balance:

1.5 1.2y 5.7+5.7 +5.7

7.2 1.2y1.21.2

y 6

1.5 1.2y 5.7

1.5 1.2(6) 5.7

1.5 7.2 5.7

1.5 1.5 ✓

2)

Practice: Binder Paper

10 5 n4–5–5

5 n4

(-4)(-4)

n 20

What should you do first?

5 4g 3+ 3+ 3

What should you do first?

0.5x 12 6–12 –12

What should you do first?

6a3

7–6 –6

What would you do second?

(3) (3)

What should you do first?

34

38x 32

32

32

( )8( )8

What should you do first?

27j 17

314

17

17

( )14 ( ) 14