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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?

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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 – 21 -8x -8x -2x + 3 = x = -24 ÷-2 ÷-2 x = 12

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3-3: Equations with variables on both sides YY OUR T URN SSolve 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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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 - 1.5h -1.5h 40 = 2h ÷2 ÷2 20 = h

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3-3: Equations with variables on both sides YYour Turn AA 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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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 – 8a6m – 5 = 6m a +8a -6m -6m 10 = 10-5 = 7 IdentityNo Solution

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3-3: Equations with variables on both sides YY OUR T URN DDetermine whether each equation is an identity or whether it has no solution n = 5n – 1 No solution 9 + 5x = 7x + 9 – 2x Identity

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

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