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Professor Fraser

Techniques for Multi-Step Equations

Slide Duration:Table of Contents

I. Basic Concepts

Variables and Expressions

24m 5s

- Intro0:00
- Definitions0:20
- Variable0:27
- Algebraic Expression2:21
- Arithmetic Operations2:27
- Lecture Example 17:16
- Lecture Example 28:27
- Additional Example 3-1
- Additional Example 4-2

Order of Operations

22m 16s

- Intro0:00
- Why We Need It0:15
- Example: Order of Operations1:25
- Procedure To Evaluate3:22
- Lecture Example 16:45
- Lecture Example 210:55
- Additional Example 3-1
- Additional Example 4-2

The Distributive Property

16m 27s

- Intro0:00
- The Distributive Property0:20
- Extension to Several Numbers2:05
- Lecture Example 12:50
- Lecture Example 25:15
- Additional Example 3-1
- Additional Example 4-2

The Real Number System

22m 35s

- Intro0:00
- The Real Number System0:21
- Natural Numbers0:22
- Whole Numbers0:37
- Integers1:06
- Rational Numbers1:35
- Example: Decimals2:07
- The Real Number System, Cont.5:00
- Square Roots5:10
- Principle Square Root6:04
- Irrational Numbers6:35
- The Real Number System, Cont.9:11
- Picture Representation9:25
- Lecture Example 111:54
- Lecture Example 214:10
- Additional Example 3-1
- Additional Example 4-2

Functions and Graphs

27m 49s

- Intro0:00
- Functions0:30
- Definition0:30
- Example: Square Roots1:18
- Example: Gas Prices3:20
- Graphs4:03
- Definition4:03
- Example: Square Roots4:48
- Domain and Range9:30
- Definition9:30
- Example: Square Roots10:01
- Lecture Example 111:22
- Lecture Example 213:58
- Additional Example 3-1
- Additional Example 4-2

II. Solving Linear Equations

From Sentences to Equations

22m 13s

- Intro0:00
- Strategy1:40
- Using Variables1:55
- Translating Phrases2:18
- Equality3:00
- Lecture Example 13:52
- Lecture Example 28:36
- Additional Example 3-1
- Additional Example 4-2

Addition and Subtraction Techniques

14m 39s

- Intro0:00
- Techniques0:22
- Adding the Same Number0:28
- Example0:47
- Subtracting the Same Number1:50
- Example1:54
- Strategy2:36
- Isolate the Variable2:46
- Lecture Example 13:48
- Lecture Example 25:41
- Additional Example 3-1
- Additional Example 4-2

Multiplication and Division Techniques

19m 19s

- Intro0:00
- Techniques0:16
- Multiplied by the Same Number0:18
- Example0:26
- Divided by the Same Number1:23
- Non-zero Exception1:28
- Dividing by Zero2:17
- Example3:01
- Strategy3:51
- Isolate the Variable3:55
- Lecture Example 14:55
- Lecture Example 26:40
- Additional Example 3-1
- Additional Example 4-2

Techniques for Multi-Step Equations

19m 13s

- Intro0:00
- What are Multi-step Equations?0:08
- Strategy0:30
- Opposite Operations0:50
- Last Operation1:18
- Lecture Example 11:54
- Lecture Example 24:16
- Additional Example 3-1
- Additional Example 4-2

When the Variable is on Both Sides of the Equation

24m 16s

- Intro0:00
- Solving More Complicated Equations0:17
- Distributive Property and Grouping Symbols0:36
- Combining0:51
- Moving Variables to One Side1:06
- Posibble Outcomes1:50
- Exactly One Solution2:02
- No Solution2:35
- Example2:51
- Identities-True for All Real Numbers4:26
- Example4:45
- Lecture Example 16:17
- Lecture Example 29:39
- Additional Example 3-1
- Additional Example 4-2

Ratios and Proportions

22m 39s

- Intro0:00
- Definitions0:16
- Ratio0:21
- Proportion0:56
- Example1:13
- Cross Products3:00
- Example: Original Proportion3:12
- Example 25:24
- Rates6:55
- Example: Gas7:22
- Example 2: Apples7:43
- Example 3: Speed8:16
- Example 4: Cookies8:46
- Lecture Example 19:17
- Lecture Example 211:53
- Additional Example 3-1
- Additional Example 4-2

Applications of Percents

20m 38s

- Intro0:00
- Definitions0:22
- Percent of Change0:23
- Percent of Increase0:42
- Percent of Decrease0:55
- Examples of Percent of Change1:14
- Sales Tax1:21
- Discount1:57
- Lecture Example 12:51
- Lecture Example 24:46
- Additional Example 3-1
- Additional Example 4-2

More Than One Variable

22m 34s

- Intro0:00
- More Than One Variable0:21
- Strategy1:02
- Typical Application1:33
- Example: Circumference1:48
- Example: Perimeter2:21
- Lecture Example 12:53
- Lecture Example 25:43
- Additional Example 3-1
- Additional Example 4-2

III. Functions

Relations

24m 39s

- Intro0:00
- Definition0:17
- List, Table, Graph0:42
- Example: List0:56
- Example: Table2:00
- Example: Graph2:47
- Domain and Range4:10
- Inverse of a Relation5:01
- Example5:21
- Lecture Example 17:26
- Lecture Example 210:39
- Additional Example 3-1
- Additional Example 4-2

Functions

19m 3s

- Intro0:00
- Definition0:21
- Function0:24
- Example: Relation0:50
- Vertical Line Test1:48
- Example: Pass2:02
- Example 2: Fail3:32
- Example 3: Fail4:18
- Function Notation5:33
- Proper Notation5:43
- Example6:29
- Domain and Range7:32
- Lecture Example 18:06
- Lecture Example 29:39
- Additional Example 3-1
- Additional Example 4-2

Linear Functions

20m 3s

- Intro0:00
- Definition0:12
- Linear Equation0:15
- Example: A and B not zero0:27
- Example: B is zero0:58
- Example: A is zero1:13
- Graph and Intercepts1:43
- Straight Line1:52
- x-intercepts, y-intercepts2:19
- Example: Intercepts2:27
- Graphing Linear Equations4:19
- Example4:40
- Linear Functions7:23
- Example8:00
- Lecture Example 110:11
- Lecture Example 212:42
- Additional Example 3-1
- Additional Example 4-2

IV. Linear Functions and their Graphs

Slope and Rate of Change

23m 58s

- Intro0:00
- Rate of Change0:27
- Independent Variable0:37
- Dependent Variable0:51
- Slope2:02
- Example2:19
- Steepness of the Line4:56
- Possible Slopes5:58
- Positive6:13
- Negative6:34
- Zero6:50
- Undefined7:11
- Lecture Example 18:03
- Lecture Example 210:34
- Additional Example 3-1
- Additional Example 4-2

Direct Variation

13m 18s

- Intro0:00
- Definitions0:13
- Direct Variation0:14
- Constant of Variation0:26
- Graph1:02
- Example: Positive and Negative k1:18
- Applications1:49
- Lecture Example 12:16
- Lecture Example 24:39
- Additional Example 3-1
- Additional Example 4-2

Slope Intercept Form of an Equation

17m 11s

- Intro0:00
- Slope Intercept Form0:16
- Example0:37
- Lecture Example 12:24
- Lecture Example 25:43
- Additional Example 3-1
- Additional Example 4-2

Point Slope Form of an Equation

10m 32s

- Intro0:00
- Point Slope Form0:11
- Example0:50
- Lecture Example 12:03
- Lecture Example 23:03
- Additional Example 3-1
- Additional Example 4-2

Parallel and Perpendicular Lines

18m 15s

- Intro0:00
- Parallel Lines0:12
- Example: Non-vertical Lines0:32
- Perpendicular lines1:57
- Example: Slope Product is -12:15
- Negative Reciprocal3:08
- Lecture Example 13:58
- Lecture Example 27:12
- Additional Example 3-1
- Additional Example 4-2

V. Systems of Equations

Graphing Systems of Equations

20m 1s

- Intro0:00
- System of Equations0:09
- Definition0:15
- Solution0:59
- Solving by Graphing1:27
- Example2:33
- Number of Solutions3:37
- Independent3:58
- Dependent4:03
- Inconsistent4:08
- Example: 1 Solution4:15
- Example: No Solution4:34
- Example: Infinite Solution4:51
- Lecture Example 15:39
- Lecture Example 28:51
- Additional Example 3-1
- Additional Example 4-2

Solving by Substitution

24m 12s

- Intro0:00
- Substitution0:17
- Example0:51
- Number of Solutions1:43
- Infinite Solutions2:14
- No Solutions2:50
- Lecture Example 13:40
- Lecture Example 26:56
- Additional Example 3-1
- Additional Example 4-2

Solving by Addition and Subtraction

12m 18s

- Intro0:00
- Fundamental Principle0:18
- Adding or Subtracting0:50
- Lecture Example 11:23
- Lecture Example 24:03
- Additional Example 3-1
- Additional Example 4-2

Solving by Multiplication

19m 11s

- Intro0:00
- Fundamental Principle0:24
- Multiplication0:28
- Lecture Example 11:40
- Lecture Example 26:36
- Additional Example 3-1
- Additional Example 4-2

Applications: Systems of Equations

18m 24s

- Intro0:00
- Solving Systems of Equations0:08
- Graphing0:32
- Addition0:50
- Subtraction1:04
- Multiplication1:13
- Substitution1:30
- Lecture Example 13:20
- Lecture Example 24:27
- Additional Example 3-1
- Additional Example 4-2

VI. Inequalities

Inequalities: Addition and Subtraction Techniques

10m 8s

- Intro0:00
- Fundamental Principle0:11
- Solutions of Inequalities0:55
- Inequality1:02
- Set Builder Notation1:13
- Example1:15
- Graph on a Number Line2:13
- Lecture Example 13:29
- Lecture Example 25:14
- Additional Example 3-1
- Additional Example 4-2

Inequalities: Multiplication and Division Techniques

10m 59s

- Intro0:00
- Fundamental Principle0:11
- Example: Positive Number0:51
- Fundamental Principle1:35
- Example: Negative Number1:50
- Lecture Example 14:05
- Lecture Example 25:12
- Additional Example 3-1
- Additional Example 4-2

Techniques for Multi-Step Inequalities

16m 21s

- Intro0:00
- Similarity to Multi-step Equations0:15
- Inequalities Containing Grouping Symbols1:03
- Special Cases1:26
- Solution: All Real Numbers1:40
- Solution: Empty Set2:16
- Lecture Example 12:54
- Lecture Example 24:37
- Additional Example 3-1
- Additional Example 4-2

Compound Inequalities

23m

- Intro0:00
- Inequalities Combined by 'And'0:12
- Three Ways to Write Solution Set1:41
- Set Notation2:01
- Inequalities2:12
- Graph2:29
- Examples2:31
- Inequalities Combined by 'Or'4:45
- Example5:59
- Lecture Example 17:40
- Lecture Example 210:55
- Additional Example 3-1
- Additional Example 4-2

Equations with Absolute Values

23m 13s

- Intro0:00
- Absolute Value0:15
- Example: Distance1:00
- Absolute Value Function2:34
- Example3:05
- Lecture Example 14:57
- Lecture Example 28:28
- Additional Example 3-1
- Additional Example 4-2

Inequalities with Absolute Values

17m 34s

- Intro0:00
- Inequalities of the Form |x|< n0:22
- Inequalities of the Form |x|> n3:30
- Lecture Example 15:33
- Lecture Example 28:50
- Additional Example 3-1
- Additional Example 4-2

Graphing Inequalities with Two Variables

30m 50s

- Intro0:00
- Graph0:22
- Half-Plane0:28
- Boundary1:37
- Technique for Graphing3:14
- Example4:01
- Dashed Line5:13
- Solid Line6:30
- Technique for Graphing, cont.8:58
- Example9:09
- Lecture Example 112:19
- Lecture Example 215:48
- Additional Example 3-1
- Additional Example 4-2

Graphing Systems of Inequalities

27m 38s

- Intro0:00
- System of Inequalities0:26
- Example0:43
- Solving a System of Inequalities1:17
- Example1:41
- Lecture Example 12:58
- Lecture Example 27:22
- Additional Example 3-1
- Additional Example 4-2

VII. Polynomials

Multiplying Monomials

19m 55s

- Intro0:00
- What is a Monomial?0:43
- Constant1:11
- Power1:48
- Exponent and Base2:39
- Properties of Exponents3:02
- Simplified Form5:52
- Each Base Appears Exactly Once6:02
- No Powers of Powers6:18
- All Fractions Simplified6:33
- Lecture Example 16:43
- Lecture Example 28:12
- Additional Example 3-1
- Additional Example 4-2

Dividing Monomials

23m 9s

- Intro0:00
- Properties of Exponents0:26
- Example1:07
- Properties of Exponents, cont2:18
- Example3:18
- Properties of Exponents, cont4:55
- Example5:32
- Properties of Exponents, cont8:49
- Lecture Example 111:43
- Lecture Example 213:13
- Additional Example 3-1
- Additional Example 4-2

Polynomials

16m 35s

- Intro0:00
- What is a Polynomial0:45
- Monomial0:47
- Example: Trinomial1:46
- Trinomial2:10
- Example: Binomial2:21
- Binomial2:30
- Degree of a Polynomial4:28
- Example4:40
- Ordering Polynomials6:45
- Example7:27
- Lecture Example 19:27
- Lecture Example 210:31
- Additional Example 3-1
- Additional Example 4-2

Adding and Subtracting Polynomials

22m

- Intro0:00
- Adding Polynomials0:36
- Like Polynomials0:48
- Example1:04
- Subtracting Polynomials3:55
- Example4:01
- Lecture Example 15:30
- Lecture Example 28:04
- Additional Example 3-1
- Additional Example 4-2

Multiplying Polynomials by Monomials

24m 8s

- Intro0:00
- Distributive Property0:22
- Basic Principle0:42
- Example1:04
- Solving Equations3:25
- Lecture Example 14:26
- Lecture Example 27:51
- Additional Example 3-1
- Additional Example 4-2

Multiplying Polynomials

26m 37s

- Intro0:00
- Distributive Property0:23
- Example0:34
- Example1:55
- Foil Method5:17
- Lecture Example 17:44
- Lecture Example 210:15
- Additional Example 3-1
- Additional Example 4-2

Special Products

19m 40s

- Intro0:00
- Square of a Sum0:12
- Perfect Square Trinomial1:43
- Example2:13
- FOIL Technique3:09
- Square of a Difference3:38
- Example5:27
- Difference of Two Squares6:12
- Example7:43
- Lecture Example 18:51
- Lecture Example 211:06
- Additional Example 3-1
- Additional Example 4-2

VIII. Factoring

Factoring Monomials

27m 25s

- Intro0:00
- Prime and Composite Numbers1:01
- Prime Number1:23
- Composite Number3:03
- Factored Forms4:07
- Prime Factored Form4:19
- Factored Form5:40
- Greatest Common Factor (GCF)7:41
- Example8:00
- GCF of Monomials10:07
- Example10:18
- Lecture Example 112:52
- Lecture Example 217:08
- Additional Example 3-1
- Additional Example 4-2

Factoring Using Greatest Common Factor (GCF)

26m 3s

- Intro0:00
- Distributive Property0:19
- Factor Out an Expression1:21
- Example2:52
- Factoring by Grouping4:40
- Example6:00
- Zero Product Property8:24
- Example9:03
- Lecture Example 111:19
- Lecture Example 214:19
- Additional Example 3-1
- Additional Example 4-2

Factoring Trinomials with Leading Coefficient 1

27m 37s

- Intro0:00
- Factoring Trinomials0:23
- Example2:06
- Rules for Signs6:27
- Both Positive6:41
- Both Negative7:00
- Opposite Signs7:33
- Solving Equations8:26
- Example8:59
- Lecture Example 111:14
- Lecture Example 214:01
- Additional Example 3-1
- Additional Example 4-2

Factoring General Trinomials

34m 11s

- Intro0:00
- Factoring Trinomials0:40
- Example: List1:38
- Grouping5:46
- Example5:55
- Rules for Signs9:04
- Example9:22
- Greatest Common Factor (GCF)10:29
- Prime Polynomials11:03
- Example11:32
- Solving Equations12:32
- Lecture Example 113:11
- Lecture Example 218:37
- Additional Example 3-1
- Additional Example 4-2

Factoring the Difference of Two Squares

20m 22s

- Intro0:00
- Difference of Two Squares0:40
- Example1:56
- Factoring Using Several Techniques3:33
- Solving Equations4:11
- Lecture Example 14:55
- Lecture Example 26:05
- Additional Example 3-1
- Additional Example 4-2

Factoring Perfect Squares

18m 7s

- Intro0:00
- Perfect Squares0:10
- Perfect Square Trinomials1:17
- Solving Equations2:53
- Square Root Property2:58
- Example3:06
- Lecture Example 14:23
- Lecture Example 26:56
- Additional Example 3-1
- Additional Example 4-2

IX. Quadratic Functions

Graphing Quadratic Functions

28m 5s

- Intro0:00
- Parabolas0:09
- Parabolas That Open Upward3:58
- Minimum4:26
- Parabolas That Open Downward4:54
- Maximum5:09
- Vertex7:28
- Example8:01
- Axis of Symmetry11:03
- Lecture Example 113:27
- Lecture Example 217:17
- Additional Example 3-1
- Additional Example 4-2

Solving Equations by Graphing

28m 18s

- Intro0:00
- Solving a Quadratic Equation0:22
- Example0:50
- Two Distinct Solutions/Roots5:08
- One Double Root5:58
- No Real Roots7:14
- Estimating Solutions8:00
- Example8:16
- Example8:31
- Lecture Example 19:43
- Lecture Example 214:10
- Additional Example 3-1
- Additional Example 4-2

Solving Equations by Completing the Square

25m 7s

- Intro0:00
- Perfect Square Trinomials0:22
- Example1:12
- Completing the Square3:17
- Example3:25
- Solving Equations6:12
- Example6:27
- Leading Coefficient is 18:25
- Lecture Example 110:23
- Lecture Example 214:17
- Additional Example 3-1
- Additional Example 4-2

Solving Equations Using the Quadratic Formula

24m 15s

- Intro0:00
- Quadratic Formula1:26
- Example2:23
- Discriminant4:28
- Two Distinct Real Roots5:07
- One Double Real Root5:23
- No Real Root5:42
- Why Does It Work?6:05
- Lecture Example 17:53
- Lecture Example 211:50
- Additional Example 3-1
- Additional Example 4-2

X. Radical Expressions and Equations

Simplifying Radical Expressions

32m 40s

- Intro0:00
- Radical Expressions0:14
- Radicand0:28
- Example0:32
- Simplest Form1:07
- Example1:35
- Product Property2:34
- Verifications2:47
- Square Roots of Variables with Even Powers4:27
- Quotient Rule6:45
- Example6:55
- Rationalizing Denominators7:32
- Example7:41
- Conjugates10:44
- Examples10:59
- Simplest Radical Form14:44
- Example15:39
- Lecture Example 117:34
- Lecture Example 219:38
- Additional Example 3-1
- Additional Example 4-2

Operations with Radical Expressions

19m 59s

- Intro0:00
- Adding and Subtracting Radical Expressions0:12
- Example0:19
- Multiplying Radical Expressions1:53
- Example2:07
- Lecture Example 15:29
- Lecture Example 26:36
- Additional Example 3-1
- Additional Example 4-2

Solving Radical Equations

26m 50s

- Intro0:00
- Radical Equations0:22
- Example0:33
- Solving a Radical Equation2:04
- Example2:16
- Extraneous Solutions3:14
- Example4:31
- Lecture Example 17:33
- Lecture Example 29:45
- Additional Example 3-1
- Additional Example 4-2

Pythagorean Theorem

19m 8s

- Intro0:00
- Right Triangles0:51
- Right Angle1:03
- Vertex1:11
- Symbol1:16
- Hypotenuse and Legs1:42
- Pythagorean Theorem2:27
- Example2:47
- Example3:12
- Pythagorean Triples4:03
- Converse of the Pythagorean Theorem6:39
- Example7:41
- Lecture Example 18:57
- Lecture Example 210:05
- Additional Example 3-1
- Additional Example 4-2

Distance Formula

18m 27s

- Intro0:00
- Distance Formula0:17
- Missing Coordinates1:46
- Example1:55
- Lecture Example 14:10
- Lecture Example 25:57
- Additional Example 3-1
- Additional Example 4-2

XI. Rational Expressions and Equations

Inverse Variation

14m 43s

- Intro0:00
- Inverse Variation0:23
- Constant of Variation0:37
- Graphing Inverse Variation1:08
- Example: Hyperbola1:15
- Product Rule3:54
- Lecture Example 15:31
- Lecture Example 27:43
- Additional Example 3-1
- Additional Example 4-2

Rational Expressions

32m 43s

- Intro0:00
- Rational Expression0:55
- Example1:03
- Excluded Values1:29
- Examples1:40
- Simplifying Rational Expressions5:36
- Greatest Common Factor (GCF)5:46
- Example5:55
- Example7:42
- Simplifying and Excluded Values9:34
- Lecture Example 19:50
- Lecture Example 213:55
- Additional Example 3-1
- Additional Example 4-2

Multiplying Rational Expressions

27m 22s

- Intro0:00
- Procedure0:16
- Example0:33
- Cancel Before Multiplication3:44
- Example3:55
- Rational Expressions Containing Polynomials6:19
- Example6:26
- Lecture Example 111:09
- Lecture Example 215:39
- Additional Example 3-1
- Additional Example 4-2

Dividing Rational Expressions

28m 30s

- Intro0:00
- Procedure0:21
- Example0:59
- Cancel Before Multiplication4:31
- Example4:39
- Rational Expressions Containing Polynomials8:01
- Example8:08
- Lecture Example 110:43
- Lecture Example 213:46
- Additional Example 3-1
- Additional Example 4-2

Dividing Polynomials

29m 44s

- Intro0:00
- Dividing a Polynomial by a Monomial1:07
- Example1:14
- Dividing a Polynomial by a Binomial3:30
- Example3:51
- Long Division5:20
- Example6:25
- Missing Terms11:11
- Example12:25
- Lecture Example 114:54
- Lecture Example 216:35
- Additional Example 3-1
- Additional Example 4-2

Adding and Subtracting Rational Expressions with Like Denominators

16m 50s

- Intro0:00
- Adding with Like Denominators0:14
- Example0:41
- Subtraction with Like Denominators2:23
- Example2:30
- Denominators That Are Additive Inverses2:55
- Example3:03
- Lecture Example 16:41
- Lecture Example 27:09
- Additional Example 3-1
- Additional Example 4-2

Adding and Subtracting Rational Expressions with Unlike Denominators

36m

- Intro0:00
- Least Common Multiple (LCM) of Polynomials0:34
- Example0:45
- Example1:55
- Adding and Subtracting4:08
- Example4:45
- Lecture Example 18:13
- Lecture Example 210:22
- Additional Example 3-1
- Additional Example 4-2

Complex Fractions

18m 43s

- Intro0:00
- Mixed Expression0:08
- Example0:30
- Complex Fraction2:45
- Example2:57
- Example3:11
- Example3:22
- Simplifying Complex Fractions3:58
- Why Does It Work?4:22
- Lecture Example 14:48
- Lecture Example 28:44
- Additional Example 3-1
- Additional Example 4-2

Rational Equations

39m 10s

- Intro0:00
- Definition0:08
- Examples0:17
- Solving Rational Expressions3:02
- Example3:09
- Work Problems6:31
- Example6:48
- Extraneous Solutions13:12
- Example14:13
- Lecture Example 117:21
- Lecture Example 219:59
- Additional Example 3-1
- Additional Example 4-2

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0 answers

Post by Shah rain on January 22, 2013

Well to me he is one of the best teacher of Algebra on Educator.com. this is his confidence because other teachers have notes but he is doing it .................... and its natural you can make mistake and a mistake when you know every thing doesn't look bad. He is the best teacher i'm enjoing his classes and learning a lot. Thanks!

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Post by Joyce Andrews-McKinney on May 23, 2012

the the error in example 3 should be deleted even though it was pretty humorous to watch.

0 answers

Post by Valdo Ribeiro on December 17, 2011

I am indeed amazed when I consider how weak my mind is and how prone to error.

Rene Descartes

0 answers

Post by shawn mallory on September 20, 2011

How would you solve 6=a/4+2?

0 answers

Post by Allison Kraus on February 7, 2011

I was able to use the Example 2 strategy on a quiz and I was really happy when I found the correct answer, which is a sign that I'm beginning to understand more. Example 3 needs to be removed, it just confused me even more and it takes up too much time.