# Solving Multi-Step/Distributive Equations - PowerPoint PPT Presentation

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Solving Multi-Step/Distributive Equations. a (b + c) = ab + ac 5 (3 + 7) = 5(3) + 5(7) = 15 + 35 = 50 . Remember that distributive property is about sharing. Example 1. Solve 5y + 2(y – 3) = 22 5y + 2y – 2(3) = 22 5y + 2y – 6 = 22

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Solving Multi-Step/Distributive Equations

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## Solving Multi-Step/Distributive Equations

a (b + c) = ab + ac

5 (3 + 7) = 5(3) + 5(7)

= 15 + 35

= 50

Remember that distributive property is about sharing.

### Example 1

• Solve

5y + 2(y – 3) = 22

5y + 2y – 2(3)= 22

5y + 2y – 6 = 22

7y – 6 = 22

7y + 0 = 28

7y = 28

y = 4

• 1st – Do the distributive Property

• 2nd – Combine family

• 3rd – Solve for x

• eliminate (+/-)

• eliminate (x/division)

+6

+6

7

7

5m + 3(m+ 5) = 31

6y + 5(2y – 4) = 12

2x + 2(2x – 5) = 38

a + 3(4a + 12) = 75

3b + 2(b + 7) = 69

Practices

m= 2

y= 2

x= 8

a= 3

b = 11

### Example 2

• Solve

13= 4(3x – 7) + 5

13 = 4(3x) – 4(7) + 5

13 = 12x – 28 + 5

13 = 12x – 23

36 = 12x + 0

36 = 12x

3=x or x=3

• 1st – Do the distributive Property

• 2nd – Combine family

• 3rd – Solve for x

• eliminate (+/-)

• eliminate (x/division)

+23

+23

12

12

47= 3(m+ 5) + 5m

7= 3(3x – 9) + x

42= 6(2y+ 5) – 9y

71= 7(3m+ 5) – 15m

48= 3(2n+ 5) + 5n

Practices

m= 4

x = 3

y = 4

m = 6

n = 3

### Example 3

1

• Solve

3 – (x – 2) = 4

3 -1(x) -1(-2)= 4

3 – x + 2 = 4

5 – x = 4

0 – x = -1

-1x = -1

x = 1

-5

-5

• 1st – Do the distributive Property

• 2nd – Combine family

• 3rd – Solve for x

• eliminate (+/-)

• eliminate (x/division)

1

-1

-1

5m – (3m+ 5) = 13

6y – 5(2y – 4) = 12

2x – 2(2x – 5) = 18

2a – 3(-4a + 12) = -8

3b – 2(b – 7) = 69

Practices

m= 9

y= -4

x= -14

a= 2

b =55

### Example 4

• Solve

5y +½ (y – 3) = 20 ½

5y + ½ y – ½ (3)= 20 ½

5m – ½ (4m+ 10) = 13

6y – ¼ (8y – 4) = 11

2x – ½ (2x – 12) = 18

2a – ¼ (-4a + 12) = -9

3b – 8(b – 7) = 71

Practices

m= 6

y= 6

x= 12

a= 4

b =-3

## Homework

Textbook Pages 148

Problems 16-36

All

### Homework

• 5m + 3(m+ 2) = 30

• 6y + 2(2y – 4) = 6

• 2x + 2(5x – 5) = 38

• 4a + 3(4a + 12) = 44

• 3b + 2(b – 7) = 104

• 103= 3(m+ 5) + 5m

• 33= 3(3x – 9) + x

• 45= 6(2y+ 5) – 9y

• 77= 7(3m+ 5) – 15m

• 59= 3(2n+ 5) + 5n

• 5m – (3m+ 5) = 45

• 6y – 5(2y – 4) = 20

• 2x – 2(2x – 5) =22

• 6a – 3(-4a + 5) = -8

• 3b – 2(b – 4) = 35

• 8m – (3m+ 5) = 35

• 6y – 5(2y – 4) = 62

• 2x – 2(2x – 5) = 8

• 2a – 3(4a + 12) = 4

• 3b – 2(b – 7) = 69

• M=3

• y = 1

• x =14

• a = 2

• T = 6

• M = 11

• X=5

• Y= 5

• M= 7

• N= 4

• m = 20

• y = 0

• J = -6

• P = 7/18

• T = 43

• M = 6

• D = 66

• J = 9

• P = -10

• T = 55