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**3-3: Equations with Variables on Both Sides**

Essential Question: How is solving an equation with variables on both sides of an equal sign different than solving an equation with variables on the same side of an equal sign? 3-3: Equations with Variables on Both Sides

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**3-3: Equations with variables on both sides**

To solve an equation that has variables on both sides, use addition or subtraction properties to get all variables to one side of the equation. Example 1: Variables on both sides Solve: 6x + 3 = 8x – 21 6x + 3 = 8x – x x -2x + 3 = -2x = -24 ÷-2 ÷-2 x = 12

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**3-3: Equations with variables on both sides**

Your Turn Solve each equation -6d = d + 4 d = -4/7 2(c – 6) = 9c + 2 c = -2 m – 5 = 3m m = -5/2 7k – 4 = 5k + 16 k = 10

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**3-3: Equations with variables on both sides**

Example 2: Real-World Problem Solving Renting in-line skates and safety equipment costs $3.50 an hour, and renting only safety equipment costs $1.50/hour. You can buy used in-line skates from your friend for $40, or you can rent some. Either way, you must rent safety equipment. How many hours must you skate for the cost of renting and buying skates to be the same? h = 3.5h h h 40 = 2h ÷2 ÷2 20 = h

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**3-3: Equations with variables on both sides**

Your Turn A hairdresser is considering ordering a certain shampoo. Company A charges $4 per 8-oz bottle plus $10 shipping per order. Company B charges $3 per 8-oz bottle plus $25 shipping per order. How many bottles must the hairdresser buy to justify using company B? 15 bottles

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**3-3: Equations with variables on both sides**

If all variables get eliminated and… The remaining statement is true, it is an identity. The remaining statement is false, the equation has no solution. Example 4 10 – 8a = 2(5 – 4a) 6m – 5 = 7m + 7 – m 10 – 8a = 10 – 8a 6m – 5 = 6m a a m m 10 = = 7 Identity No Solution

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**3-3: Equations with variables on both sides**

Your Turn Determine whether each equation is an identity or whether it has no solution. 9 + 5n = 5n – 1 No solution 9 + 5x = 7x + 9 – 2x Identity

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**3-3: Equations with variables on both sides**

Assignment Practice 3-3 1 – 35, odd problems Quiz tomorrow on 3-1 & 3-2

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Identities, Contradictions and Conditional Equations.

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