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**Multiplying or Dividing 2-2**

Solving Equations by Multiplying or Dividing 2-2 Hand in HW – p 80 to front table 2-2 Notes, HW p 87 # 21-44, Holt Algebra 1

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Objective I will: Solve one-step equations in one variable by using multiplication or division.

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**Solving Equations Using Multiplication**

2-2 Solving Equations by Multiplying or Dividing Course 3 Solving Equations Using Multiplication Think…. What type of problem is this and how do I “undo” it? b –4 Solve = 5. b –4 = 5 –4 • • –4 Multiply both sides by –4. b = –20 Check b –4 = 5 –20 –4 = 5 ? Substitute –20 for b. 5 = 5 ?

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**2-2 Solving Equations by Multiplying or Dividing**

Course 3 Check It Out: Example 2 c –3 Solve = 5. c –3 = 5 –3 • • –3 Multiply both sides by –3. c = –15 Check c –3 = 5 –15 –3 = 5 ? Substitute –15 for c. 5 = 5 ?

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**Example 2A: Solving Equations by Using Division**

Solve the equation. Check your answer. 9y = 108 Since y is multiplied by 9, divide both sides by 9 to undo the multiplication. y = 12 Check 9y = 108 To check your solution, substitute 12 for y in the original equation. 9(12) 108

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**Example 2B: Solving Equations by Using Division**

Solve the equation. Check your answer. –4.8 = –6v Since v is multiplied by –6, divide both sides by –6 to undo the multiplication. 0.8 = v Check –4.8 = –6v –4.8 –6(0.8) To check your solution, substitute 0.8 for v in the original equation. –4.8 –4.8

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Check It Out! Example 2a Solve the equation. Check your answer. 16 = 4c Since c is multiplied by 4, divide both sides by 4 to undo the multiplication. 4 = c Check = 4c 16 4(4) To check your solution, substitute 4 for c in the original equation.

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Check It Out! Example 2c Solve the equation. Check your answer. 15k = 75 Since k is multiplied by 15, divide both sides by 15 to undo the multiplication. k = 5 Check 15k = 75 To check your solution, substitute 5 for k in the original equation. 15(5) 75

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**Remember that dividing is the same as multiplying by the reciprocal.**

Instead of dividing by a fraction to get the variable alone, you multiply both sides by the reciprocal.

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**What is the reciprocal of:**

5/6 2 -9/8

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**Example 3A: Solving Equations That Contain Fractions**

Solve the equation. 5 w = 20 6 The reciprocal of is Since w is multiplied by , multiply both sides by 5 6 w = 24 Check w = 20 5 6 To check your solution, substitute 24 for w in the original equation. 20 20 20

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**Example 3B: Solving Equations That Contain Fractions**

Solve the equation. 3 1 8 = z 16 The reciprocal of is 8. Since z is multiplied by , multiply both sides by 8. 1 8 = z 3 2 Check 1 8 3 16 = z To check your solution, substitute for z in the original equation. 3 2 3 16

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**Solve the equation. Check your answer. 1 4 1 5 – = b**

Check It Out! Example 3a Solve the equation. Check your answer. 1 4 1 5 – = b The reciprocal of is 5. Since b is multiplied by , multiply both sides by 5. 1 5 = b 5 4 – = b 5 4 Check 1 – To check your solution, substitute – for b in the original equation. 5 4

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Definition A mathematical sentence, that shows that two expressions, either numerical or algebraic, are equivalent. Like a balance. Characteristics Isolate.

Definition A mathematical sentence, that shows that two expressions, either numerical or algebraic, are equivalent. Like a balance. Characteristics Isolate.

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