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Dr. Carleen Eaton

Dr. Carleen Eaton

Graphing Inequalities with Two Variables

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Table of Contents

I. Basic Concepts
Variables and Expressions

11m 22s

Intro
0:00
History of Algebra
0:12
Origin of Word
0:21
Real World Problems
0:35
Definitions
0:58
Variable
1:03
Algebraic Expression
1:37
Operations
2:02
Example 1: Words into Expressions
3:02
Example 2: Words into Expressions
5:20
Example 3: Words into Expressions
6:45
Example 4: Words into Expressions
9:46
Order of Operations

15m 59s

Intro
0:00
Example
0:17
Definition
0:57
Procedure to Evaluate an Arithmetic Expression
1:08
Grouping Symbols (Parentheses, Brackets, Braces)
1:19
Powers
1:42
Multiply/Divide Left to Right
1:57
Add/Subtract Left to Right
2:21
Example: Fraction Bar
2:49
Example 1: Evaluate Arithmetic Expression
3:45
Example 2: Evaluate Arithmetic Expression
7:28
Example 3: Evaluate Arithmetic Expression
10:11
Example 4: Evaluate with Variables
13:12
Distributive Property

9m 50s

Intro
0:00
Distributive Property Statements
0:23
Moving Forward
0:49
Rule for Subtraction
1:14
Reverse Order
1:40
Several Numbers
2:17
Example 1: Evaluate Using Distributive Property
2:56
Example 2: Multiply Using Distributive Property
4:10
Example 3: Simplify Using Distributive Property
4:59
Example 4: Simplify Using Distributive Property
7:03
Real Number System

17m 58s

Intro
0:00
Real Number System
0:31
Natural Numbers
0:39
Whole Numbers
1:11
Integers
1:23
Rational Numbers
1:52
Cannot Divide by Zero
2:18
Decimals
2:27
Example: Terminating or Repeating
2:39
Real Number System, Cont.
3:37
Square Roots
3:42
Examples
3:54
Irrational Numbers
4:36
Examples
5:02
Perfect Square
5:54
Real Number System, Cont.
6:49
Example: Number Line
7:02
Example 1: Which Set of Numbers
7:54
Example 2: Graph on Number Line
10:04
Example 3: Approximate Irrational Number
12:47
Example 4: Order Largest to Smallest
13:57
Functions and Graphs

34m 39s

Intro
0:00
Functions
0:15
Example: Function
0:29
Example: Not Functions (Relations)
1:15
Graphs
4:44
Visual Display
4:53
Example: X and Y
5:03
Coordinate Pairs
5:53
Discrete Function
8:19
Continuous Function
8:55
Vertical Line Test
10:55
Test if Function
11:12
Example: Pass Through Points
11:43
Domain and Range
14:13
Example
14:43
Example 1: Function Given by Table
16:24
Example 2: Cost of Gas
18:46
Example 3: Cost of Gas
23:15
Example 4: Cost of Mail
29:07
II. Solving Linear Equations
From Sentences to Equations

16m 5s

Intro
0:00
Real World Applications
0:18
Strategy
0:26
Using Variables
0:32
Translate Phrases
0:48
Identity Equality Words
1:07
Example 1: Write Equation
1:32
Example 2: Write Equation
4:14
Example 3: Sisters' Ages
8:26
Example 4: Surface Area of Cylinder
12:52
Addition and Subtraction Techniques

15m 24s

Intro
0:00
Techniques
0:21
Addition Principle
0:24
Example
0:37
Subtraction Principle
1:44
Example
1:48
Strategy
2:33
Isolate the Variable
2:41
Example
2:55
Example 1: Solve Equation
3:39
Example 2: Solve Equation
5:38
Example 3: Word Problem
7:38
Example 4: Word Problem
11:14
Multiplication and Division Techniques

15m 41s

Intro
0:00
Isolating the Variable
0:08
Techniques
0:34
Multiplication Principle
0:41
Example
0:57
Division Principle
2:32
Example
2:47
Strategy
3:12
Example
3:30
Opposite Operation
3:53
Example 1: Solve Equation
5:07
Example 2: Solve Equation
6:50
Example 3: Solve Equation
10:05
Example 4: Word Problem
12:07
Techniques for Multistep Equations

14m 31s

Intro
0:00
What are Multistep Equations
0:06
Addition/Subtraction and Multiplication/Division
0:31
Strategy
0:43
Identify Last Operation
0:47
Example 1: Solve Equation
1:51
Example 2: Solve Equation
5:27
Example 3: Find Numbers
7:39
Example 4: Solve Equation
11:27
When the Variable is on Both Sides of the Equation

20m 17s

Intro
0:00
Solving More Complicated Equations
0:28
Distributive Property
0:41
Review of Distributive Property
0:55
Factoring
1:28
Subtracting
1:50
Applying with Addition/Subtraction
2:08
Possible Outcomes
2:45
Exactly One Solution
2:52
No Solution
3:08
True for All Real Numbers
4:45
Identities
5:01
Example 1: Solve Equation
6:03
Example 2: Solve Equation
9:08
Example 3: Solve Equation
14:06
Example 4: Solve Equation
17:28
Ratios and Proportion

16m 5s

Intro
0:00
Definitions
0:07
Ratio
0:10
Different Representations
0:14
Proportion
0:33
Example
0:40
Cross Product
1:08
Cross Multiplication
1:32
Example
2:13
Rates
3:33
Rates in Real Life
3:46
Example 1: Form a Proportion
4:43
Example 2: Cross Multiply
7:15
Example 3: How Long to Drive
9:00
Example 4: Cross Products
12:13
Applications of Percents

13m 46s

Intro
0:00
Definitions
0:15
Percent of Increase
0:27
Percent of Decrease
0:34
Examples
0:42
Sales Tax
1:48
Discount
2:44
Example 1: Temperature Change
3:12
Example 2: Sales Tax
5:44
Example 3: Clothing Discount
7:04
Example 4: Sales and Discount
9:15
More Than One Variable

20m 38s

Intro
0:00
More Than One Variable
0:21
Real Life Examples
0:30
Strategy
1:08
Possible Techniques
1:17
Typical Application
1:43
Solving for a Different Variable
1:59
Example 1: Solve for Y
5:06
Example 2: Solve for Q
7:38
Example 3: Solve for H
12:56
Example 4: Solve for X
16:04
III. Functions
Relations

16m 58s

Intro
0:00
Definition
0:04
Relation
0:06
Table
0:18
Set of Ordered Pairs
1:01
Graph
1:38
Domain and Range
2:40
Example: Relation
2:51
Example: Broader Cases
3:48
Inverse of a Relation
4:42
Example
4:59
Example 1: Relation as Table/Graph
6:15
Example 2: Domain and Range
8:41
Example 3: Table, Graph, Domain, Range
10:36
Example 4: Inverse of a Relation
13:36
Functions

19m 27s

Intro
0:00
Definition
0:14
Review of Relations
0:27
Violation of Function
1:43
Example: Function
2:00
Vertical Line Test
3:18
Example
3:41
Function Notation
6:15
Using f(x)
6:26
Example: Value Assigned
7:12
Example 1: Relation a Function
8:10
Example 2: Relation a Function
9:39
Example 3: Using f(x) Notation
12:20
Example 4: g(x) Notation
15:01
Linear Functions

20m 15s

Intro
0:00
Definition
0:07
Standard Form
0:18
Example
0:52
Graph and Intercepts
2:39
Example: Graph
2:48
X-Intercept
2:56
Y-Intercept
3:35
Graphing Linear Equations
4:29
Example
4:47
Linear Functions
7:51
Example
8:15
Example 1: Linear
10:16
Example 2: Linear Equation
12:58
Example 3: Intercepts
14:23
Example 4: Equation from Intercepts
16:47
IV. Linear Functions and Their Graphs
Slope and Rate of Change

19m 46s

Intro
0:00
Rate of Change
0:06
Other Words
0:14
Example
0:24
Slope
2:12
Two Points
2:39
Steepness of a Line
2:57
Possible Slopes
4:29
Positive Slope
5:02
Negative Slope
5:29
Zero Slope (Horizontal Line)
6:23
Undefined Slope (Vertical Line)
7:08
Example 1: Rate of Change of Table
8:19
Example 2: Slope Through Points
10:52
Example 3: Increasing/Decreasing
13:06
Example 4: Slope Through Points
16:02
Direct Variation

13m 54s

Intro
0:00
Definitions
0:10
Constant of Variation k
0:21
Example: Gas and Miles Driven
0:59
Graph
1:50
k is Slope
2:04
Examples
2:27
Applications
2:47
Write, Graph, Solve
2:58
Example 1: Constant of Variation
3:11
Example 2: Graph Direct Variation
4:59
Example 3: Direct Variation
6:50
Example 4: Distance Car Travels
9:18
Slope Intercept Form of an Equation

12m 6s

Intro
0:00
Slope Intercept Form
0:12
m (Slope) and b (Y Intercept)
0:31
Example
1:12
Example 1: Slope Intercept Form Equation
2:39
Example 2: Graph the Equation
5:11
Example 3: Slope Intercept Form Equation
6:51
Example 4: Slope Intercept Form Equation
8:50
Point Slope Form of an Equation

9m 7s

Intro
0:00
Point Slope Form
0:07
Manipulating to Other Forms
0:35
m (Slope), x1 y1 (Point)
0:47
Example 1: Point Slope Form Equation
1:03
Example 2: Point Slope Form Equation
2:50
Example 3: Point Slope Form Equation
4:18
Example 4: Point Slope Form Equation
6:50
Parallel Lines and Perpendicular Lines

18m 2s

Intro
0:00
Parallel Lines
0:08
Example
0:15
Vertical Lines
0:40
Perpendicular Lines
1:19
Negative Reciprocal
1:31
Example
2:05
Example 1: Slope Intercept Form
3:25
Example 2: Parallel or Perpendicular
6:15
Example 3: Slope Intercept Form
9:27
Example 4: Slope Intercept Form
12:35
V. Systems of Equations
Graphing Systems of Equations

22m 45s

Intro
0:00
Systems of Equations
0:10
Definition
0:15
Example
0:31
Solution
0:47
Solving by Graphing
1:23
Points of Intersection
1:36
Example
1:56
Number of Solutions
3:09
Independent
3:20
Dependent
3:50
Inconsistent
4:46
Example 1: Solve by Graphing
5:45
Example 2: Solve by Graphing
9:50
Example 3: Solve by Graphing
14:17
Example 4: Solve by Graphing
18:03
Solving by Substituting

22m 41s

Intro
0:00
Substitution
0:09
Example
0:45
Number of Solutions
2:47
Infinite Solutions
3:11
No Solutions
4:28
Example 1: Solve by Substitution
5:44
Example 2: Solve by Substitution
10:01
Example 3: Solve by Substitution
15:17
Example 4: Solve by Substitution
19:41
Solving by Addition and Subtraction

16m 13s

Intro
0:00
Fundamental Principle
0:10
Example
0:23
Example 1: Solve the System
1:52
Example 2: Solve the System
5:53
Example 3: Solve the System
10:15
Example 4: Solve the System
14:08
VI. Inequalities
Addition & Subtraction Techniques

11m 34s

Intro
0:00
Fundamental Principle
0:09
Example
0:36
Solutions of Inequalities
1:51
Inequality
1:59
Set Builder Notation
2:02
Graph on a Number Line
2:08
Examples
2:18
Example 1: Solve the Inequality
4:59
Example 2: Solve the Inequality
7:00
Example 3: Solve the Inequality
8:10
Example 4: Solve the Inequality
9:47
Multiplication & Division Techniques

10m 49s

Intro
0:00
Fundamental Principle
0:10
Only Positive Numbers
0:23
Example
0:51
Fundamental Principle, Cont.
2:01
Negative Numbers
2:12
Reverse Inequality Sign
2:28
Example
2:48
Example 1: Solve the Inequality
4:26
Example 2: Solve the Inequality
5:45
Example 3: Solve the Inequality
6:50
Example 4: Solve the Inequality
8:28
Techniques for Multistep Inequalities

16m 56s

Intro
0:00
Similarity to Multistep Equations
0:16
Negative Numbers
0:32
Example
0:49
Inequalities Containing Grouping Symbols
1:24
Example
1:35
Special Cases
2:45
Example: All Real Numbers
3:04
Example: Empty Set
4:10
Example 1: Solve the Inequality
6:05
Example 2: Solve the Inequality
7:39
Example 3: Solve the Inequality
9:57
Example 4: Solve the Inequality
13:56
Compound Inequalities

21m 32s

Intro
0:00
What is a Compound Inequality
0:07
Joined by 'And' or 'Or'
0:16
Inequalities Combined by 'And'
0:36
Intersection/Overlap
0:53
Example
1:08
Inequalities Combined by 'Or'
4:23
Union
4:41
Example
5:27
Example 1: Solve the Inequality
6:39
Example 2: Solve the Inequality
11:30
Example 3: Solve the Inequality
13:43
Example 4: Solve the Inequality
18:19
Equations with Absolute Value

24m 16s

Intro
0:00
Absolute Value
0:06
Number Line
0:22
Example
0:41
Absolute Value is N
1:52
Absolute Value Function
3:17
Example
3:40
g(x) and f(x)
4:31
Solving Absolute Value Equations
6:23
Absolute Value in Words
6:39
Split Into Two Parts
7:58
Solve Both Equations
8:22
Example 1: Solve the Absolute Value
10:34
Example 2: Solve the Absolute Value
13:09
Example 3: Solve the Absolute Value
14:52
Example 4: Solve the Absolute Value
20:23
Inequalities with Absolute Values

17m 37s

Intro
0:00
Inequalities of the Form |x|< n
0:07
Values that Satisfy Both Inequalities
0:46
Example
1:27
Inequalities of the Form |x|> n
3:58
Values that Satisfy Either Inequalities
4:19
Example
4:47
Example 1: Solve the Inequality
6:38
Example 2: Solve the Inequality
9:54
Example 3: Solve the Inequality
12:05
Example 4: Solve the Inequality
14:50
Graphing Inequalities with Two Variables

24m 33s

Intro
0:00
Graph
0:08
Half Plane and Boundary
0:51
Technique for Graphing
1:57
Graph Equation
2:01
Solid Line or Dashed Line
2:07
Example
2:32
Choosing a Test Point
5:10
Example
5:26
Example 1: Solve the Inequality
7:49
Example 2: Solve the Inequality
11:37
Example 3: Solve the Inequality
15:44
Example 4: Solve the Inequality
19:10
Graphing Systems of Inequalities

24m 4s

Intro
0:00
System of Inequalities
0:05
Example
0:22
Solving a System of Inequalities
0:38
Solution Set
0:46
Graph Each Inequality
0:57
Area of Overlap
1:45
Example 1: Solve the System of Inequalities
2:44
Example 2: Solve the System of Inequalities
6:33
Example 3: Solve the System of Inequalities
11:40
Example 4: Solve the System of Inequalities
17:36
VII. Polynomials
Multiplying Monomials

22m 19s

Intro
0:00
What is a Monomial
0:09
Examples
0:17
Power
0:55
Base and Exponent
1:52
Properties of Exponents
2:16
Add Exponents
2:25
Multiply Exponents
4:00
Product Exponent
4:39
Simplified Form
7:26
Examples
7:47
Example 1: Simplify the Monomial
8:26
Example 2: Simplify the Monomial
10:32
Example 3: Simplify the Monomial
12:48
Example 4: Simplify the Monomial
17:33
Dividing Monomials

24m 2s

Intro
0:00
Properties of Exponents
0:05
Dividing with Same Base
0:15
Example
0:53
Quotient Raised to Power
2:22
Example
2:53
Raising to 0 Power
4:00
Example
4:21
Negative Exponents
5:45
Example
6:05
Example 1: Simplify the Monomial
7:33
Example 2: Simplify the Monomial
14:56
Example 3: Simplify the Monomial
13:30
Example 4: Simplify the Monomial
17:35
Polynomials

8m 56s

Intro
0:00
What is a Polynomial
0:07
Monomial
0:40
Binomial
1:15
Trinomial
1:25
Degree of a Polynomial
1:56
Example: Degree of Monomial
2:13
Example: Degree of Polynomial
2:47
Ordering Polynomials
3:32
Example
3:47
Example 1: Trinomial or Binomial
4:44
Example 2: Find the Degree
5:27
Example 3: Increasing Powers
6:11
Example 4: Decreasing Powers
7:27
Adding and Subtracting Polynomials

15m 51s

Intro
0:00
Adding Polynomials
0:07
Like Terms
0:18
Example
1:02
Subtracting Polynomials
2:44
Example
2:58
Example 1: Add Polynomials
5:11
Example 2: Subtract Polynomials
7:30
Example 3: Add and Subtract
9:35
Example 4: Add and Subtract
12:09
Multiplying Polynomials by Monomials

18m 17s

Intro
0:00
Distributive Property
0:07
Example
0:54
Solving Equations
1:36
Isolate Variable and Solve
1:46
Example 1: Multiply
1:59
Example 2: Simplify
3:33
Example 3: Simplify
7:20
Example 4: Solve
13:37
Multiplying Polynomials

18m 2s

Intro
0:00
Distributive Property
0:08
Example
0:54
FOIL Method
2:44
First, Outer, Inner, Last
3:20
Example 1: Multiply
5:32
Example 2: Multiply
7:27
Example 3: Multiply
9:41
Example 4: Multiply
13:56
Special Products

17m

Intro
0:00
Square of a Sum
0:06
Example
1:09
Square of a Difference
2:46
Example
3:22
Difference of Two Squares
4:50
Example
5:31
Example 1: Multiply
6:24
Example 2: Multiply
8:34
Example 3: Multiply
11:03
Example 4: Multiply
12:54
VIII. Factoring
Special Product

17m 51s

Intro
0:00
Prime and Composite Numbers
0:09
Prime Number
0:12
Composite Number
0:42
Factored Forms
1:39
Prime Factored Form
1:40
Factored Form
2:21
Greatest Common Factor
3:55
Example: GCF for Number
4:19
Example: GCF for Monomial
6:00
Example 1: Prime Factored Form
7:51
Example 2: Factored Form
9:34
Example 3: GCF
11:12
Example 4: GCF
13:28
Factoring Using Greatest Common Factor

25m 21s

Intro
0:00
Distributive Property
0:05
Example: Binomial
0:49
Example: Trinomial
2:18
Factoring by Grouping
4:17
Example: Four Terms
4:40
Zero Product Property
8:21
Example
9:01
Example 1: Factor the Polynomial
10:38
Example 2: Factor the Polynomial
13:43
Example 3: Factor the Polynomial
19:59
Example 4: Solve the Polynomial
22:58
Factoring Trinomials with Leading Coefficient of 1

27m 11s

Intro
0:00
Factoring Trinomials
0:07
Leading Coefficient
0:11
Example
1:20
Rules for Signs
2:42
P and Q Both Positive
2:55
P and Q Both Negative
3:39
P and Q Opposite Signs
4:30
Solving Equations
5:18
Example
6:44
Example 1: Factor the Polynomial
7:41
Example 2: Factor the Polynomial
12:33
Example 3: Factor the Polynomial
16:39
Example 4: Solve the Polynomial
21:35
Factoring General Trinomials

46m 9s

Intro
0:00
Factoring Trinomials
0:15
Example
2:42
Grouping
7:20
Example
7:35
Rules for Signs
10:51
Same as Leading Coefficient is 1
11:05
Greatest Common Factor
12:29
Use Whenever Possible
12:41
Example
12:59
Prime Polynomials
13:58
Example
14:33
Solving Equations
16:55
Example
17:25
Example 1: Factor the Polynomial
18:46
Example 2: Factor the Polynomial
25:23
Example 3: Factor the Polynomial
32:37
Example 4: Solve the Polynomial
36:18
Factoring the Difference of Two Squares

24m 3s

Intro
0:00
Difference of Two Squares
0:08
Example
0:36
Factoring Using Several Techniques
2:23
Factoring the GCF
2:30
Example
3:22
Solving Equations
5:24
Example
5:50
Example 1: Factor the Polynomial
7:34
Example 2: Factor the Polynomial
9:11
Example 3: Factor the Polynomial
12:00
Example 4: Solve the Polynomial
18:31
Factoring Perfect Squares

18m 10s

Intro
0:00
Perfect Squares
0:07
Example: Perfect Square Trinomials
1:12
Solving Equations
2:57
Square Root Property
3:09
Example
3:28
Example 1: Factor the Polynomial
5:09
Example 2: Factor the Polynomial
6:13
Example 3: Solve the Polynomial
8:43
Example 4: Solve the Polynomial
13:35
IX. Quadratic Functions
Graphing Quadratic Functions

35m 45s

Intro
0:00
Parabolas
0:14
Standard Form of Quadratic Function
0:28
Examples
1:05
Absolute Value of 'a'
2:19
Parabolas That Open Upward
3:14
Minimum
3:48
Example
3:57
Parabolas That Open Downward
6:57
Example
7:17
Maximum
9:23
Vertex
9:53
Example
10:40
Axis of Symmetry
14:16
Example
15:03
Example 1: Graph the Quadratic
19:54
Example 2: Graph the Quadratic
24:12
Example 3: Vertex Maximum or Minimum
28:32
Example 4: Axis of Symmetry
31:13
Solving Equations by Graphing

40m 42s

Intro
0:00
Solving a Quadratic Equation
0:08
Example
0:56
Two Distinct Solutions/Roots
8:10
Roots
8:23
Example: Graphs
8:40
One Double Root
9:19
Example: One X-Intercept
9:54
No Real Roots
14:03
Example
14:53
Estimating Solutions
18:41
Example: Not Integers
19:18
Example 1: Solve by Graphing
20:18
Example 2: Solve by Graphing
26:36
Example 3: Solve by Graphing
30:18
Example 4: Estimate by Graphing
34:59
Solving Equations by Completing the Square

28m 13s

Intro
0:00
Perfect Square Trinomials
0:15
Example
0:36
Completing the Square
4:55
Example
6:20
Completing the Square to Solve Equations
9:19
Example
9:40
When the Leading Coefficient is Not 1
13:17
Example
14:01
Example 1: Solve the Equation
15:05
Example 2: Complete the Square
20:16
Example 3: Solve by Completing the Square
22:31
Example 4: Solve by Completing the Square
25:02
Solving Equations Using the Quadratic Formula

17m 17s

Intro
0:00
Quadratic Formula
0:17
Standard Form
0:24
Example
1:00
Discriminant
3:14
Two Solutions and Both Real
3:40
One Real Solution
4:07
No Real Solutions
4:28
Example 1: Solve the Equation
6:25
Example 2: Solve the Equation
8:42
Example 3: Solve the Equation
12:02
Example 4: Number of Real Roots
15:23
X. Radical Expressions and Equations
Simplifying Radical Expressions

41m 30s

Intro
0:00
Radical Expression
0:12
Example: Radicand Simplest Form
0:29
Example: Not Simplest Form
1:16
Principal Square Root (Positive)
2:43
Product Property
3:40
Examples
4:05
Square Roots of Variables with Even Powers
7:01
Eliminate Radical Sign
7:42
Divide Exponent by 2
7:57
Absolute Value of Result
8:29
Examples
8:52
Quotient Rule
14:12
Example
14:31
Rationalizing Denominators
16:08
Example
16:43
Conjugates
18:33
Example
19:53
Simplest Radical Form
20:58
Three Criteria
21:10
Example 1: Simplify Expression
21:57
Example 2: Simplify Expression
25:12
Example 3: Simplify Expression
31:37
Example 4: Simplify Expression
35:29
Operations with Radical Expressions

21m 52s

Intro
0:00
Adding and Subtracting Radical Expressions
0:13
Like Radicals
0:28
Distributive Property
1:10
Multiplying Radical Expressions
4:24
Example: Use FOIL
4:44
Example 1: Simplify Expression
7:07
Example 2: Simplify Expression
8:51
Example 3: Simplify Expression
12:14
Example 4: Simplify Expression
16:06
Solving Radical Equations

27m

Intro
0:00
Radical Equations
0:15
Examples
0:30
Solving a Radical Equation
1:13
Isolate Radical
1:18
Square Both Sides
1:38
Example
1:44
Extraneous Solutions
2:57
Example: Check Solutions
3:30
Example 1: Solve Equation
6:29
Example 2: Solve Equation
9:52
Example 3: Solve Equation
14:29
Example 4: Solve Equation
20:53
Pythagorean Theorem

17m 24s

Intro
0:00
Right Triangles
0:06
Vertex
0:32
Hypotenuse
0:56
Legs
1:11
Pythagorean Theorem
1:21
Graphical Representation
1:37
Example
2:39
Pythagorean Triples
3:40
Example
3:56
Converse of the Pythagorean Theorem
4:36
Example
6:23
Example 1: Length of Hypotenuse
7:24
Example 2: Length of Legs
9:02
Example 3: Area of Triangle
12:00
Example 4: Length of Side
14:59
Distance Formula

26m 50s

Intro
0:00
Distance Formula
0:09
Similarity to Pythagorean Theorem
0:21
Missing Coordinates
5:50
Example
6:22
Example 1: Distance Between Points
11:43
Example 2: Distance Between Points
14:05
Example 3: Distance Between Points
18:18
Example 4: Missing Coordinate
21:57
XI. Rational Expressions and Equations
Inverse Variation

24m 13s

Intro
0:00
Direct Variation
0:12
Inverse Variation
0:24
Constant of Variation k
0:50
Y Varies Inversely as X
0:59
Graphing Inverse Variation
3:09
Real World Applications
3:24
Example
3:59
Product Rule
10:19
Alternate Form
11:10
Finding Missing 4th Point
11:24
Example 1: Graph Inverse Variation
11:36
Example 2: Graph Inverse Variation
14:47
Example 3: Find Missing Point
19:39
Example 4: Find Missing Point
21:53
Rational Expressions

34m 22s

Intro
0:00
Rational Expressions
0:10
Examples
0:28
Excluded Values
1:03
Dividing by 0
1:29
Example
2:49
Simplifying Rational Expressions
7:12
Eliminating the GCF
7:17
Example: Regular Fraction
7:30
Example: Rational Expression
8:12
Simplifying and Excluded Values
10:15
Original Rational Expression
10:24
Example
10:47
Example 1: Find Excluded Values
13:47
Example 2: Simplify and Find Excluded Values
16:10
Example 3: Simplify and Find Excluded Values
22:04
Example 4: Simplify and Find Excluded Values
26:29
Multiplying Rational Expressions

22m 58s

Intro
0:00
Procedure
0:08
Examples
0:29
Cancel Before Multiplication
1:53
Example
2:04
Rational Expressions Containing Polynomials
3:18
Example
3:46
Example 1: Multiply Rational Expressions
6:04
Example 2: Multiply Rational Expressions
9:11
Example 3: Multiply Rational Expressions
11:19
Example 4: Multiply Rational Expressions
17:36
Dividing Rational Expressions

21m 49s

Intro
0:00
Procedure
0:10
Reciprocal of Expression
0:22
Example: Regular Fractions
0:44
Example: Rational Expressions
1:46
Cancel Before Multiplying
3:23
Why Cancel
3:45
Example
4:15
Rational Expressions Containing Polynomials
6:46
Example
7:06
Example 1: Divide Rational Expressions
9:15
Example 2: Divide Rational Expressions
13:11
Example 3: Divide Rational Expressions
15:39
Dividing Polynomials

35m 57s

Intro
0:00
Dividing a Polynomial by a Monomial
0:11
Example: Regular Fractions
0:36
Example: Polynomials
1:24
Dividing a Polynomial by a Binomial
2:56
Example: Dividend and Divisor
3:30
Long Division
5:28
Example: Regular Numbers
5:49
Example: Polynomials
7:17
Missing Terms
12:20
Definition
12:40
Example
12:55
Example 1: Divide the Polynomials
18:42
Example 2: Divide the Polynomials
20:54
Example 3: Divide the Polynomials
23:28
Example 4: Divide the Polynomials
28:52
Adding and Subtracting Rational Expressions with Like Denominators

17m 38s

Intro
0:00
Adding with Like Denominators
0:09
Example: Regular Numbers
0:19
Example: Rational Expressions
1:05
Subtracting with Like Denominators
2:35
Example: Regular Fractions
2:52
Example: Rational Expressions
3:05
Denominators That Are Additive Inverses
4:08
What Are Additive Inverses
4:35
Example
5:53
Example 1: Add Rational Expressions
7:54
Example 2: Subtract Rational Expressions
8:43
Example 3: Add Rational Expressions
10:39
Example 4: Subtract Rational Expressions
11:48
Adding and Subtracting Rational Expressions with Unlike Denominators

37m 16s

Intro
0:00
Least Common Multiple of Polynomials
0:21
Example: Regular Fractions
0:42
Example: Rational Expressions
5:18
Equivalent Rational Expressions Using LCM
7:23
Example
8:09
Adding and Subtracting
14:24
Summary of Techniques
14:32
Example 1: Find the LCM
15:09
Example 2: Add Rational Expressions
17:53
Example 3: Subtract Rational Expressions
22:19
Example 4: Add Rational Expressions
30:44
Complex Fractions

25m 38s

Intro
0:00
Mixed Expressions
0:10
Analogy to Mixed Fractions
0:23
Polynomial and Rational Expression
0:59
Example: Combining
1:55
Converting to Rational Expression
2:29
Complex Fraction
5:16
Examples
5:30
Simplifying Complex Fractions
6:08
Example
6:27
Example 1: Write as Rational Expression
9:43
Example 2: Simplify Complex Fractions
12:44
Example 3: Simplify Complex Fractions
15:03
Example 4: Simplify Complex Fractions
19:55
Rational Equations

38m 9s

Intro
0:00
Definition
0:11
Example: Cross Multiplication
0:39
Example: Rational Expressions
1:13
Solving Rational Equations
3:12
Multiply by LCM of Denominators
3:33
Example
4:02
Work Problems
7:19
Example: Complete a Project
8:17
Extraneous Solutions
12:41
Check All Solutions
13:18
Example
13:54
Example 1: Solve Rational Equation
17:28
Example 2: Solve Rational Equation
19:45
Example 3: Work Problem
27:15
Example 4: Solve Rational Equation
31:10
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