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6.1
Order of Operations
Copyright © 2009 Pearson Education, Inc.
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Definitions
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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:
4x  2
x, x  4, 4(3 y  5),
, y 2  8y  2
3x  5
Copyright © 2009 Pearson Education, Inc.
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Order of Operations
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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Example: Evaluating an Expression
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Evaluate the expression x2 + 4x + 5 for x = 3.
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Solution:
x2 + 4x + 5
= 32 + 4(3) + 5
= 9 + 12 + 5
= 26
Copyright © 2009 Pearson Education, Inc.
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Practice Problems: p. 295 # 12 & 20
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Example: Substituting for Two Variables
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Evaluate 4 x 2  3 xy  5y 2 when x = 3 and y = 4.
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Solution:
4 x 2  3 xy  5 y 2
 4(3)2  3(3)(4)  5(4 2 )
 4(9)  36  5(16)
 36  36  80
 0  80
 80
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P. 295 # 24
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Example 3: Determine whether the
value is a solution to the equation
6x – 7 = -31, x = -4
6(-4) – 7 = -31
-24 – 7 = -31
-31= -31
Yes, x = -4 is a solution.
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Practice Problems: p. 295 # 36
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Homework
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P. 295 # 9 – 45 odd (show all work)
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