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College Algebra Math 130 Amy Jones Lewis

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Comp-U-Us You and two of your friends have decided to start a new company, Comp-U-Us, to assemble and sell computers. So far you have assembled 20 computers. Your friend has just taken an order from a large local company that has agreed to purchase a number of computers from your company. Your sales prices is $1,800 per computer.

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Comp-U-Us Define a variable for the additional number of computers you will be assembling (in addition to the 20 computers already assembled). Use the variable to write an expression for the total number of computers that your company will have assembled. Write an expression for the total income your company will receive for all the computers that will be assembled. How can you write this expression a different way?

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Comp-U-Us How much will your company receive if you assemble and sell: 20 additional computers? 50 additional computers? 100 additional computers? 200 additional computers? To have a total income of $576,000, how many additional computers must you assemble? Explain how you found this answer.

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Comp-U-Us Labels Computers to be Assembled Total Computers Total Income Units Computers Expression 20 50 100 200

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Comp-U-Us The scenario shows that: 1800(x +20) = 1800x + 1800·20 The “law” or rule that says these two expressions are equal is called the Distributive Property. Look at the left side of the equation. Explain what was done to arrive at the right side of the equation.

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The Distributive Property Use the distributive Property to rewrite each expression as a sum or difference: Example: 5(x+11) = 5x + 55 1. 2(x + 3) 2. (x – 10)(100) 3. 5(7 – 3x) 4. x(x + 3) 5. (30 – 20x)(5) 6. 2(2x + 14) 7. 7(5x – 7)

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The Distributive Property Factoring is the “undoing” of the Distributive Property. For example, 5x – 20 can be rewritten as 5(x – 4). Factor these expressions: 1. 2x + 6 2. 7x – 21 3. 100x – 1000 4. -14x + 21 5. 32 – 24x 6. 35x – 112 7. x 2 + 3x

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Homework Next Class: Monday, November 1

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