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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. 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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  1. 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.

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. Example 4 • Solve 5y +½ (y – 3) = 20 ½ 5y + ½ y – ½ (3)= 20 ½

  9. 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

  10. Homework Textbook Pages 148 Problems 16-36 All

  11. 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

  12. 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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