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**Learn to solve equations that have variables on both sides.**

Course 2 12-3 Solving Equations with Variables on Both Sides Learn to solve equations that have variables on both sides.

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**Solving Equations with Variables on Both Sides**

Course 2 12-3 Solving Equations with Variables on Both Sides Additional Example 1: Using Inverse Operations to Group Terms with Variables Group the terms with variables on one side of the equal sign, and simplify. A. 60 – 4y = 8y 60 – 4y = 8y 60 – 4y + 4y = 8y + 4y Add 4y to both sides. 60 = 12y Simplify. B. –5b + 72 = –2b –5b + 72 = –2b –5b + 5b + 72 = –2b + 5b Add 5b to both sides. 72 = 3b Simplify.

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**Solving Equations with Variables on Both Sides**

Course 2 12-3 Solving Equations with Variables on Both Sides Check It Out: Example 1 Group the terms with variables on one side of the equal sign, and simplify. A. 40 – 2y = 6y 40 – 2y = 6y 40 – 2y + 2y = 6y + 2y Add 2y to both sides. 40 = 8y Simplify. B. –8b + 24 = –5b –8b + 24 = –5b –8b + 8b + 24 = –5b + 8b Add 8b to both sides. 24 = 3b Simplify.

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**Additional Example 2A: Solving Equations with Variables on Both Sides**

Course 2 12-3 Solving Equations with Variables on Both Sides Additional Example 2A: Solving Equations with Variables on Both Sides Solve. 7c = 2c + 55 7c = 2c + 55 7c – 2c = 2c – 2c + 55 Subtract 2c from both sides. 5c = 55 Simplify. 5c = 55 5 Divide both sides by 5. c = 11

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**Additional Example 2B: Solving Equations with Variables on Both Sides**

Course 2 12-3 Solving Equations with Variables on Both Sides Additional Example 2B: Solving Equations with Variables on Both Sides Solve. 49 – 3m = 4m + 14 49 – 3m = 4m + 14 49 – 3m + 3m = 4m + 3m + 14 Add 3m to both sides. 49 = 7m + 14 Simplify. 49 – 14 = 7m + 14 – 14 Subtract 14 from both sides. 35 = 7m 35 = 7m 7 Divide both sides by 7. 5 = m

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**Additional Example 2C: Solving Equations with Variables on Both Sides**

Course 2 12-3 Solving Equations with Variables on Both Sides Additional Example 2C: Solving Equations with Variables on Both Sides 2 5 x = 1 x – 12 2 5 1 5 x = x – 12 2 5 x 15 – = 1 – 12 1 5 Subtract x from both sides. 1 5 x –12 = Simplify. 1 5 (5) x = (5)(–12) Multiply both sides by 5. x = –60

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**Solving Equations with Variables on Both Sides**

Course 2 12-3 Solving Equations with Variables on Both Sides Check It Out: Example 2A Solve. 8f = 3f + 65 8f = 3f + 65 8f – 3f = 3f – 3f + 65 Subtract 3f from both sides. 5f = 65 Simplify. 5f = 65 5 Divide both sides by 5. f = 13

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**Solving Equations with Variables on Both Sides**

Course 2 12-3 Solving Equations with Variables on Both Sides Check It Out: Example 2B Solve. 54 – 3q = 6q + 9 54– 3q = 6q + 9 54 – 3q + 3q = 6q + 3q + 9 Add 3q to both sides. 54 = 9q + 9 Simplify. 54 – 9 = 9q + 9 – 9 Subtract 9 from both sides. 45 = 9q 45 = 9q 9 Divide both sides by 9. 5 = q

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**Solving Equations with Variables on Both Sides**

Course 2 12-3 Solving Equations with Variables on Both Sides Check It Out: Example 2C Solve. 2 3 w = 1 w – 9 2 3 1 3 w = w – 9 1 3 2 3 w 13 – = 1 – 9 Subtract w from both sides. 1 3 w –9 = Simplify. 1 3 (3) w = (3)(–9) Multiply both sides by 3. w = –27

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