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**Solving Equations with variables on both sides of the Equals**

Chapter 3.5

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**Solving Equations with variables on both sides of the Equals**

Lesson Objective: NCSCOS Use linear functions to model and solve problems Students will know how to solve equations with variables on both sides. Students will know how to use the distributive property to solve problems. Students will know how to combine like terms to solve problems

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**Solving Equations with variables on both sides of the Equals**

5x - 8 = 3x + 12 Example 1: First we must get all the variables on one side of the equation. Subtract 3x from both sides -3x x 2x - 8 = 12

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2x - 8 = 12 2 x = 20 x = 10 Second we have to get all the numbers on the other side Add 8 to both sides Divide both sides by 2

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**Solving Equations with variables on both sides of the Equals**

6 – x = 5x + 30 5y – 2y = 3y + 2 4m – 8 = 10 – 2m 8 + 4k = k (2/5)x – 8 = 9 – (3/5)x Practice

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**Solving Equations with variables on both sides of the Equals**

Example 2: Distribute on both sides Add 10x to both sides 4(2x – 1) = -10(x – 5) 8x – 4 = -10x + 50 +10x x 18x – 4 = 50

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**Solving Equations with variables on both sides of the Equals**

Add 4 to both sides Divide by 18 18x – 4 = 50 18x = 54 x = 3

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**Solving Equations with variables on both sides of the Equals**

-3(x + 5) = 3(x – 1) 5(x + 2) = 2(3 – x) 4(m + 3) = 36 4(y – 2) = 2(5 – y) 3(x – 8) = 3x More Practice

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**Solving Equations with variables on both sides of the Equals**

Example 3: Distribute on both sides Combine like terms on either side of the equals sign 5(x + 3) + 9 = 3(x – 4) + 6 5x = 3x – 5x + 24 = 3x - 6

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**Solving Equations with variables on both sides of the Equals**

Subtract 3x from both sides Add 24 to both sides Divide by 2 5x + 24 = 3x - 6 2x + 24 = -6 2x = -30 x = -15

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**Solving Equations with variables on both sides of the Equals**

3(x – 8) – 5 = 9(x + 2) + 1 2(x + 2) + x = 5 + 4(x – 2) 5x – (3x – 3) = 2x + 3(x + 4) Last Practice!

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**Solving Equations with variables on both sides of the Equals**

Quiz 3.5 2x + 3 = 3x – 5 7x – 3 = 3 – 2x 2(x + 3) = 3(x – 4) 5(2x – 4) = -6(2 – x) 3(x + 2) – 2x = 4(x -3) + 6

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Solving Inequalities with variables on both sides of the Sign

Solving Inequalities with variables on both sides of the Sign

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