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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.

- 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

- 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

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

- 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

- 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