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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

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
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

slide3
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
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

slide5
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
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

slide7
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
Example 4
  • Solve

5y +½ (y – 3) = 20 ½

5y + ½ y – ½ (3)= 20 ½

slide9
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

Homework

Textbook Pages 148

Problems 16-36

All

homework1
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
answers
Answers
  • 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
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