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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.

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Presentation on theme: "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."— Presentation transcript:

1 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?

2 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

3 3-3: Equations with variables on both sides YY OUR T URN S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

4  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

5 3-3: Equations with variables on both sides YYour Turn A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

6  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

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

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


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