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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 8 Introduction to Algebra

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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 8.1 Introduction to Variables

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33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluating Algebraic Expressions A combination of numbers, letters(variables), and operation symbols is called an algebraic expression or simply an expression. 3 + x 5y2z – 1 + x Replacing a variable in an expression by a number and then finding the value of the expression is called evaluating the expression.

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44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Evaluate: 3x – 7 when x = 6 3x – 7 = 3(6) – 7 = 18 – 7 = 11

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55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Evaluate: 4x + 2y when x = 8 and y = –2 Replace x with 8 and y with –2. 4x + 2y = 4(8) + 2(–2) = 32 – 4 = 28

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66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Evaluate: 8 – (6a – 5) when a = –3.

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77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Combining Like Terms The addends in an algebraic expression are called the terms of the expression. x + 3 = 2 terms x and 3 A term that is only a number has a special name. It is called a constant term. A term that contains a variable is called a variable term. The number factor of a variable term is called the numerical coefficient.

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88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Combining Like Terms Like TermsUnlike Terms

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99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Distributive Property If a, b, and c are numbers, then ac + bc = (a + b)c Also, ac – bc = (a – b)c

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10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Simplify each expression by combining like terms. a. 4x + 8x 4x + 8x = (4 + 8)x = 12x b. y – 5y y – 5y = (1 – 5)y = –4y

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11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Properties of Addition and Multiplication If a, b, and c are numbers, then a + b = b + a or ab = ba That is, the order of adding or multiplying two numbers can be changed without changing their sum or product. (a + b) + c = a + (b + c)or(ab)c = a(bc) That is, the grouping of numbers in addition or multiplication can be changed without changing their sum or product.

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12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Simplify each expression by combining like terms. a. 4x + 8x – 7 = 12x – 7 b. 4x + 5 – 6x + 3x = 4x – 6x + 3x + 5 = x + 5 c. 3x – 4 + 5y + 3x – 9y + 12 = 6x – 4y + 8

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13 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Multiplying Expressions a. 6(4y) = 24y b. –5(5y) = –25y

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14 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Multiplying Expressions Use the distributive property to multiply: 7(x + 2) 7(x + 2) = 7x + 7(2) = 7x + 14

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15 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplifying Expressions Simplify: 4(5 + 6y) – 9 4(5 + 6y) – 9 = 4(5) + 4(6y) – 9 = 20 + 24y – 9 = 11 + 24y

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16 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Finding Perimeter and Area Example Find the perimeter and area of this basketball court. P = 2l + 2w P = 2(45) + 2(2x – 6) P = 90 + 4x – 12 P = 78 + 4x A = lw P = 45(2x – 6) P = 90x – 270

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