ch06MGF1106 - Chapter 6 Algebra, Graphs and Functions Slide...

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Slide 6 - 1 Chapter 6 Algebra, Graphs and Functions
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Slide 6 - 2 6.1 Order of Operations
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Slide 6 - 3 Definitions Algebra: a generalized form of arithmetic. Variables: letters used to represent numbers Constant: symbol that represents a specific quantity Algebraic expression: a collection of variables, numbers, parentheses, and operation symbols. Examples: 2 4 2 , 4, 4(3 5), , 8 2 3 5 x x x y y y x + + + + - -
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Slide 6 - 4 Order of Operations (PEDMAS) 1. First, perform all operations within parentheses or other grouping symbols (according to the following order). 2. Next, perform all exponential operations (that is, raising to powers or finding roots). 3. Next, perform all multiplication and divisions from left to right. 4. Finally, perform all additions and subtractions from left to right.
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Slide 6 - 5 Example 1: Evaluating an Expression Evaluate the expression x 2 + 4 x + 5 for x = 3. Solution: x 2 + 4 x + 5 = 3 2 + 4(3) + 5 = 9 + 12 + 5 = 26
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Slide 6 - 6 Example 2: Substituting for Two Variables Evaluate when x = 3 and y = 4. Solution: 2 2 4 3 5 x xy y - + - 2 2 2 2 4(3) 3(3)(4) 5(4 ) 4(9) 36 5(16) 36 36 80 0 80 8 4 3 5 0 x xy y = - + - = - + - = - + - = - - = - + -
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Slide 6 - 7 6.2 Linear Equations in One Variable
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Slide 6 - 8 Definitions Terms are parts that are added or subtracted in an algebraic expression. Coefficient is the numerical part of a term. Like terms are terms that have the same variables with the same exponents on the variables. Unlike terms have different variables or different exponents on the variables. 2 2 2 , 7 5 , 8 x x x x - 3 2 2 , 7 5 , 6 x x x -
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Slide 6 - 9 Properties of the Real Numbers Associative property of multiplication ( ab ) c = a ( bc ) Associative property of addition ( a + b ) + c = a + ( b + c ) Commutative property of multiplication ab = ba Commutative property of addition a + b = b + a Distributive property a ( b + c ) = ab + ac
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Slide 6 - 10 Example 1: Combine Like Terms 8 x + 4 x = (8 + 4) x = 12 x 5 y - 6 y = (5 - 6) y = - y x + 15 - 5 x + 9 = (1 - 5 ) x + (15 + 9) = - 4 x + 24 3 x + 2 + 6 y - 4 + 7 x = (3 + 7) x + 6 y + (2 - 4) = 10 x + 6 y - 2
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Slide 6 - 11 Solving Equations Addition Property of Equality If a = b , then a + c = b + c for all real numbers a , b , and c . Find the solution to the equation x - 9 = 24. x - 9 + 9 = 24 + 9 x = 33 Check: x - 9 = 24 33 - 9 = 24 ? 24 = 24 true
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Solving Equations continued Subtraction Property of Equality If a = b , then a - c = b - c for all real numbers a , b , and c . Find the solution to the equation x + 12 = 31. x
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This note was uploaded on 12/12/2011 for the course MGF 1106 taught by Professor Holbrook during the Spring '10 term at Santa Fe College.

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ch06MGF1106 - Chapter 6 Algebra, Graphs and Functions Slide...

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