Transcript GSBA 522a: Managerial Perspectives

Panlilio 2008-2009
Section 1.1 & 1.2 Objectives
 Use the order of operations to evaluate experations
 Use formulas
 Determine the sets of numbers to which a given
number belongs
 Use the properties of real numbers to simplify
expressions
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Order of Operations
 Please Excuse My Dear Aunt Sally
 The Order:
 1. ___________ (and other groupings like brackets or
fraction bars)
 2. ___________
 3. All Multiplication and Division from _____ to ______
 4. All Additions and Subtractions from _____ to _____
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Order of Operations
 Try these problems
2
10   4  3 2  
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7
3  5  2 
4 7  14 
6  23  7  4
Using Formulas
 When given a formula, just Plug AND Chug!
The formula for the volume of a rectangular prism is V  lwh . Find the volume of
each cylinder given the following values:
l=7, w=22, h=3
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l=2.25, w=4.1, h=3
Cube with sides of length 8
Properties of Real Numbers
Reals, R
R=
I=
Z
I
W
Q
N
Q=
Z=
W=
Rational numbers can be expressed
as a ratio m
n
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N=
Properties for Addition and
Multiplication
Addition
Commutatitve
Associative
Identity
Inverse
Distributive
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Multiplication
Name the Property
x yz yz x
4(h  2k)  4h  8k
70 7
12  3  3 12
1
(8)  1
8
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Section 1.4 & 1.5 Objectives
 Translate verbal expressions and sentences into
algebraic expressions and equations
 Solve equations by using the properties of equality
 Solve equations for a specific variable
 Solve equations containing absolute value
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Translating Words into Math
Twice the cube of a number
Three less than a number is -7
Four times the sum of a number
and 2
A number divided by 4 is 2/3
The product of a number and its
square
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Properties of Equality
For any real number a, a=a
For all real numbers a and b, if a=b,
then b=a
For all real numbers a, b, and c, if a=b
and b=c, then a=c
If a=b, then a may be replaced by b
For any numbers a, b, and c, if a=b
then a+c=b+c and a-c=b-c
For any real numbers a, b, and c, if
a b
a=b, then ab=b c and, if c0, c  c
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Solving Equations
 Solve each equation:
4n  5  11
10  4 5  3x 
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2
1
y   3
3
2
1.4c  9  2.3c  5
t  2t  3t  4t  10
5 3
1
 y
6 8
24
Absolute Value Equations
 Absolute Value of a Number --> The number of units it
is from 0 on the number line
 Absolute Value Equations --> Two Possible Scenarios:
1. The number inside is positive, or 2. The number
inside is negative. Either way, when you take the
absolute value, you get a __________.
2x  3  5
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x  14  7
9x  4  8
Section 1.6 & 1.7 Objectives
 Solve inequalities and graph the solution sets
 Solve compound inequalities using and and or
 Solve inequalities involving absolute value and graph
the solutions
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Solving Inequalities
 Solve each inequality. Graph the solution.
5y  3  2y  9
.5m  14
x3
x 
4
Reminder! When solving inequalities: if you multiply or divide by a negative number,
you have to ________ the inequality sign.
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Compound Inequalities
 “And” --> Must make
both inequalities true.
Shade the ___________.
5  2x  3  12
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 “Or” --> Can make either
inequality true. Shade
______________.
2
x  4 and 8  x  4
5
x3
 2 or 1.2x  3.3  2.3x  1.1
3
Absolute Value Inequalities
 Absolute Value Inequalities are Compound
Inequalities.
x2 4
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4x  3  9
x 1  x 1
Homework
 1.1 & 1.2: P.10 #19-51 EOO,54,56,58; P.17 #21-57 EOO,58
 1.4 & 1.5: P.31 #19-53 Odd,56,60; P.41 #17-41 EOO,45,46
 1.6 & 1.7: P.47#15-43 EOO,49,50,57-59; P.53 #15-43
EOO,45,46,49-55 Odd
 Chapter Review P.56 #1-27 Odd, #33-69 Odd
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