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Math 015 Section 6.3 Equations

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any algebra expressions on each side variable terms on one side and constants on the other side by the coefficient of the variable

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Obj: To solve an equation of the form ax + b = cx + d Problem: Solve 5x – 4 = 2x + 5 Solution: 5x – 4 = 2x + 5 5x = 2x + 5 + 4 3x = 9 x = -3 5x = 2x + 9 5x – 2x = 9 x = 9393

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Obj: To solve an equation of the form ax + b = cx + d Problem: Solve 2y – 7 = -1 – 2y Solution: 2y – 7 = -2y – 1 2y = -2y + 6 4y = 6 x = 6 4 3232

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Be sure to simplify each side before continuing the solving process. Problem: Solve 5x – 2(x + 1) = 23 Solution:5x – 2(x + 1) = 23 5x – 2x – 2 = 23 Simplify by combining like terms on the left side 3x = 25 x = 25/3 3x – 2 = 23 collect terms divide

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Be sure to simplify each side before continuing the solving process. Problem: Solve 7 – (5 – 8x) = 4x + 3 Solution:7 – (5 – 8x) = 4x + 3 7 – 5 + 8x = 4x + 3 8x = 4x + 1 x = 1/4 8x + 2 = 4x + 3 4x = 1

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F 1 x = F 2 (d – x) F 1 = weight (force) of one object F 2 = weight (force) of the second object d = length of the lever x = distance from F 1 to the fulcrum d – x = distance from F to the fulcrum

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F 1 x = F 2 (d – x) Two children are sitting on a seesaw that is 10 ft long. One child weighs 60 lb and the other child weighs 90 lb. How far from the 90 lb child should the fulcrum be placed for them to balance? 9060 x10 – x 90x = 60(10 – x ) 90x = 600 – 60x 150x = 600 x = 4 The fulcrum must be 4 ft from the 90 lb child.

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Px = Cx + F x = the number of things produced P = the selling price for each unit C = the cost to produce each unit F = the fixed cost for the business

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Px = Cx + F An economist has determined that the selling price per unit for a gas barbecue is $325. The cost to make one barbecue is $175, and the fixed cost for the factory is $39,000. Find the break-even point. 325x = 175x + 39,000 150x = 39,000 x = 260 The company must build and sell 260 barbecue units to break even

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