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**Solving Equations by Multiplying or Dividing**

Objective: Solve equations using the multiplication and division properties of equality.

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Minute Check Solve each equation. x – 3 = 5

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Minute Check Solve each equation. x – 3 = 5 8

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Minute Check Solve each equation. x – 3 = 5 y + 9 = 7

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Minute Check Solve each equation. x – 3 = 5 y + 9 = 7 -2

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Minute Check Solve each equation. x – 3 = 5 y + 9 = 7 13 = m – 6

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Minute Check Solve each equation. x – 3 = 5 y + 9 = 7 13 = m – 6 19

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**Minute Check Solve each equation. x – 3 = 5 y + 9 = 7 13 = m – 6**

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**Minute Check Solve each equation. x – 3 = 5 y + 9 = 7 13 = m – 6**

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**Minute Check Solve each equation. x – 3 = 5 y + 9 = 7 13 = m – 6**

f + 4 = -5

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**Minute Check Solve each equation. x – 3 = 5 y + 9 = 7 13 = m – 6**

f + 4 =

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**Solving Equations by Multiplying or Dividing**

Division Property of Equality For any numbers a, b, and c, where c < > 0, if a = b, then a/c = b/c.

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**Solving Equations by Multiplying or Dividing**

Example Solve 8y = 96. Check your solution.

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**Solving Equations by Multiplying or Dividing**

Example Solve 8y = 96. Check your solution. 8y/8 = 96/8 Divide each side by 8.

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**Solving Equations by Multiplying or Dividing**

Example Solve 8y = 96. Check your solution. 8y/8 = 96/8 Divide each side by 8. y = 12

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**Solving Equations by Multiplying or Dividing**

Example Solve 8y = 96. Check your solution. 8y/8 = 96/8 Divide each side by 8. y = 12 Check: 8y = 96 Replace y with 12.

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**Solving Equations by Multiplying or Dividing**

Example Solve 8y = 96. Check your solution. 8y/8 = 96/8 Divide each side by 8. y = 12 Check: 8y = 96 Replace y with 12. 8(12) ? 96

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**Solving Equations by Multiplying or Dividing**

Example Solve 8y = 96. Check your solution. 8y/8 = 96/8 Divide each side by 8. y = 12 Check: 8y = 96 Replace y with 12. 8(12) ? 96 96 = 96 The solution is 12.

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**Solving Equations by Multiplying or Dividing**

Multiplication Property of Equality For any numbers a, b, and c, if a = b, then ac = bc.

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**Solving Equations by Multiplying or Dividing**

Example 2 Solve y/-6 = 12. Check your solution.

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**Solving Equations by Multiplying or Dividing**

Example 2 Solve y/-6 = 12. Check your solution. -6 * y/-6 = -6 * 12 Multiply each side by –6

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**Solving Equations by Multiplying or Dividing**

Example 2 Solve y/-6 = 12. Check your solution. -6 * y/-6 = -6 * 12 Multiply each side by –6 y = -72

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**Solving Equations by Multiplying or Dividing**

Example 2 Solve y/-6 = 12. Check your solution. -6 * y/-6 = -6 * 12 Multiply each side by –6 y = -72 Check: y/-6 = 12 Replace y with -72

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**Solving Equations by Multiplying or Dividing**

Example 2 Solve y/-6 = 12. Check your solution. -6 * y/-6 = -6 * 12 Multiply each side by –6 y = -72 Check: y/-6 = 12 Replace y with -72 -72/-6 ? 12

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**Solving Equations by Multiplying or Dividing**

Example 2 Solve y/-6 = 12. Check your solution. -6 * y/-6 = -6 * 12 Multiply each side by –6 y = -72 Check: y/-6 = 12 Replace y with –72. -72/-6 ? 12 12 = 12 The solution is –72.

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**Solving Equations by Multiplying or Dividing**

Application: Tom has a piece of rope that is 105 feet long. He wants to cut the rope into 5 equal pieces. How long will each piece be?

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**Solving Equations by Multiplying or Dividing**

Application: Tom has a piece of rope that is 105 feet long. He wants to cut the rope into 5 equal pieces. How long will each piece be? Let L represent the length of each piece.

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**Solving Equations by Multiplying or Dividing**

Application: Tom has a piece of rope that is 105 feet long. He wants to cut the rope into 5 equal pieces. How long will each piece be? Let L represent the length of each piece. 105 = 5*L Write an equation.

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**Solving Equations by Multiplying or Dividing**

Application: Tom has a piece of rope that is 105 feet long. He wants to cut the rope into 5 equal pieces. How long will each piece be? Let L represent the length of each piece. 105 = 5*L Write an equation. 105/5 = 5*L/5 Divide each side by 5.

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**Solving Equations by Multiplying or Dividing**

Application: Tom has a piece of rope that is 105 feet long. He wants to cut the rope into 5 equal pieces. How long will each piece be? Let L represent the length of each piece. 105 = 5*L Write an equation. 105/5 = 5*L/5 Divide each side by 5. 21 = L The solution is 21.

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