Solving by Multiplication, Algebra 1

Solving by Multiplication

V. Systems of Equations: Lecture 4 | 19:11 min

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Solving by Multiplication

Sometimes you cannot get a solution by just adding or subtracting the original equations. You must first multiply one or both of the equations by appropriate constants to produce two new equations that have the same or opposite coefficients for one of the variables. Then you can add or subtract the new equations to eliminate the variable with the same or opposite coefficients. The resulting equation in one variable can be easily solved using familiar techniques. Then find the solution for the other variable by substituting the value for the first variable into either of the original equations.
Use this method if none of the coefficients is 1 or –1 and neither pair of coefficients of the same variable are the equal or opposites.

Solving by Multiplication

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

Intro

Fundamental Principle

Multiplication

Lecture Example 1

Lecture Example 2

Additional Example 3

Additional Example 4

I. Basic Concepts
	Variables and Expressions	24:05
	Order of Operations	22:16
	The Distributive Property	16:27
	The Real Number System	22:35
	Functions and Graphs	27:49
II. Solving Linear Equations
	From Sentences to Equations	22:13
	Addition and Subtraction Techniques	14:39
	Multiplication and Division Techniques	19:19
	Techniques for Multi-Step Equations	19:13
	When the Variable is on Both Sides of the Equation	24:16
	Ratios and Proportions	22:39
	Applications of Percents	20:38
	More Than One Variable	22:34
III. Functions
	Relations	24:39
	Functions	19:03
	Linear Functions	20:03
IV. Linear Functions and their Graphs
	Slope and Rate of Change	23:58
	Direct Variation	13:18
	Slope Intercept Form of an Equation	17:11
	Point Slope Form of an Equation	10:32
	Parallel and Perpendicular Lines	18:15
V. Systems of Equations
	Graphing Systems of Equations	20:01
	Solving by Substitution	24:12
	Solving by Addition and Subtraction	12:18
	Solving by Multiplication	19:11
	Applications: Systems of Equations	18:24
VI. Inequalities
	Inequalities: Addition and Subtraction Techniques	10:08
	Inequalities: Multiplication and Division Techniques	10:59
	Techniques for Multi-Step Inequalities	16:21
	Compound Inequalities	23:00
	Equations with Absolute Values	23:13
	Inequalities with Absolute Values	17:34
	Graphing Inequalities with Two Variables	30:50
	Graphing Systems of Inequalities	27:38
VII. Polynomials
	Multiplying Monomials	19:55
	Dividing Monomials	23:09
	Polynomials	16:35
	Adding and Subtracting Polynomials	22:00
	Multiplying Polynomials by Monomials	24:08
	Multiplying Polynomials	26:37
	Special Products	19:40
VIII. Factoring
	Factoring Monomials	27:25
	Factoring Using Greatest Common Factor (GCF)	26:03
	Factoring Trinomials with Leading Coefficient 1	27:37
	Factoring General Trinomials	34:11
	Factoring the Difference of Two Squares	20:22
	Factoring Perfect Squares	18:07
IX. Quadratic Functions
	Graphing Quadratic Functions	28:05
	Solving Equations by Graphing	28:18
	Solving Equations by Completing the Square	25:07
	Solving Equations Using the Quadratic Formula	24:15
X. Radical Expressions and Equations
	Simplifying Radical Expressions	32:40
	Operations with Radical Expressions	19:59
	Solving Radical Equations	26:50
	Pythagorean Theorem	19:08
	Distance Formula	18:27
XI. Rational Expressions and Equations
	Inverse Variation	14:43
	Rational Expressions	32:43
	Multiplying Rational Expressions	27:22
	Dividing Rational Expressions	28:30
	Dividing Polynomials	29:44
	Adding and Subtracting Rational Expressions with Like Denominators	16:50
	Adding and Subtracting Rational Expressions with Unlike Denominators	36:00
	Complex Fractions	18:43
	Rational Equations	39:10

Mathematics: Algebra 1

I. Basic Concepts
	Variables and Expressions			24:05
		Intro		0:00
		Definitions		0:20
			Variable	0:27
			Algebraic Expression	2:21
			Arithmetic Operations	2:27
		Lecture Example 1		7:16
		Lecture Example 2		8:27
		Additional Example 3		6:30
		Additional Example 4		6:19
	Order of Operations			22:16
		Intro		0:00
			Why We Need It	0:15
			Example: Order of Operations	1:25
		Procedure To Evaluate		3:22
		Lecture Example 1		6:45
		Lecture Example 2		10:55
		Additional Example 3		3:32
		Additional Example 4		4:27
	The Distributive Property			16:27
		Intro		0:00
		The Distributive Property		0:20
			Extension to Several Numbers	2:05
		Lecture Example 1		2:50
		Lecture Example 2		5:15
		Additional Example 3		3:10
		Additional Example 4		4:48
	The Real Number System			22:35
		Intro		0:00
		The Real Number System		0:21
			Natural Numbers	0:22
			Whole Numbers	0:37
			Integers	1:06
			Rational Numbers	1:35
			Example: Decimals	2:07
		The Real Number System, Cont.		5:00
			Square Roots	5:10
			Principle Square Root	6:04
			Irrational Numbers	6:35
		The Real Number System, Cont.		9:11
			Picture Representation	9:25
		Lecture Example 1		11:54
		Lecture Example 2		14:10
		Additional Example 3		1:00
		Additional Example 4		4:45
	Functions and Graphs			27:49
		Intro		0:00
		Functions		0:30
			Definition	0:30
			Example: Square Roots	1:18
			Example: Gas Prices	3:20
		Graphs		4:03
			Definition	4:03
			Example: Square Roots	4:48
		Domain and Range		9:30
			Definition	9:30
			Example: Square Roots	10:01
		Lecture Example 1		11:22
		Lecture Example 2		13:58
		Additional Example 3		3:59
		Additional Example 4		5:26
II. Solving Linear Equations
	From Sentences to Equations			22:13
		Intro		0:00
		Strategy		1:40
			Using Variables	1:55
			Translating Phrases	2:18
			Equality	3:00
		Lecture Example 1		3:52
		Lecture Example 2		8:36
		Additional Example 3		5:24
		Additional Example 4		4:22
	Addition and Subtraction Techniques			14:39
		Intro		0:00
		Techniques		0:22
			Adding the Same Number	0:28
			Example	0:47
			Subtracting the Same Number	1:50
			Example	1:54
		Strategy		2:36
			Isolate the Variable	2:46
		Lecture Example 1		3:48
		Lecture Example 2		5:41
		Additional Example 3		2:30
		Additional Example 4		4:58
	Multiplication and Division Techniques			19:19
		Intro		0:00
		Techniques		0:16
			Multiplied by the Same Number	0:18
			Example	0:26
			Divided by the Same Number	1:23
			Non-zero Exception	1:28
			Dividing by Zero	2:17
			Example	3:01
		Strategy		3:51
			Isolate the Variable	3:55
		Lecture Example 1		4:55
		Lecture Example 2		6:40
		Additional Example 3		3:55
		Additional Example 4		4:54
	Techniques for Multi-Step Equations			19:13
		Intro		0:00
		What are Multi-step Equations?		0:08
		Strategy		0:30
			Opposite Operations	0:50
			Last Operation	1:18
		Lecture Example 1		1:54
		Lecture Example 2		4:16
		Additional Example 3		7:19
		Additional Example 4		4:34
	When the Variable is on Both Sides of the Equation			24:16
		Intro		0:00
		Solving More Complicated Equations		0:17
			Distributive Property and Grouping Symbols	0:36
			Combining	0:51
			Moving Variables to One Side	1:06
		Possible Outcomes		1:50
			Exactly One Solution	2:02
			No Solution	2:35
			Example	2:51
			Identities-True for All Real Numbers	4:26
			Example	4:45
		Lecture Example 1		6:17
		Lecture Example 2		9:39
		Additional Example 3		4:19
		Additional Example 4		5:27
	Ratios and Proportions			22:39
		Intro		0:00
		Definitions		0:16
			Ratio	0:21
			Proportion	0:56
			Example	1:13
		Cross Products		3:00
			Example: Original Proportion	3:12
			Example 2	5:24
		Rates		6:55
			Example: Gas	7:22
			Example 2: Apples	7:43
			Example 3: Speed	8:16
			Example 4: Cookies	8:46
		Lecture Example 1		9:17
		Lecture Example 2		11:53
		Additional Example 3		4:42
		Additional Example 4		4:25
	Applications of Percents			20:38
		Intro		0:00
		Definitions		0:22
			Percent of Change	0:23
			Percent of Increase	0:42
			Percent of Decrease	0:55
		Examples of Percent of Change		1:14
			Sales Tax	1:21
			Discount	1:57
		Lecture Example 1		2:51
		Lecture Example 2		4:46
		Additional Example 3		3:25
		Additional Example 4		8:45
	More Than One Variable			22:34
		Intro		0:00
		More Than One Variable		0:21
		Strategy		1:02
		Typical Application		1:33
			Example: Circumference	1:48
			Example: Perimeter	2:21
		Lecture Example 1		2:53
		Lecture Example 2		5:43
		Additional Example 3		3:54
		Additional Example 4		8:04
III. Functions
	Relations			24:39
		Intro		0:00
		Definition		0:17
			List, Table, Graph	0:42
			Example: List	0:56
			Example: Table	2:00
			Example: Graph	2:47
		Domain and Range		4:10
		Inverse of a Relation		5:01
			Example	5:21
		Lecture Example 1		7:26
		Lecture Example 2		10:39
		Additional Example 3		5:42
		Additional Example 4		5:26
	Functions			19:03
		Intro		0:00
		Definition		0:21
			Function	0:24
			Example: Relation	0:50
		Vertical Line Test		1:48
			Example: Pass	2:02
			Example 2: Fail	3:32
			Example 3: Fail	4:18
		Function Notation		5:33
			Proper Notation	5:43
			Example	6:29
			Domain and Range	7:32
		Lecture Example 1		8:06
		Lecture Example 2		9:39
		Additional Example 3		1:37
		Additional Example 4		5:08
	Linear Functions			20:03
		Intro		0:00
		Definition		0:12
			Linear Equation	0:15
			Example: A and B not zero	0:27
			Example: B is zero	0:58
			Example: A is zero	1:13
		Graph and Intercepts		1:43
			Straight Line	1:52
			x-intercepts, y-intercepts	2:19
			Example: Intercepts	2:27
		Graphing Linear Equations		4:19
			Example	4:40
		Linear Functions		7:23
			Example	8:00
		Lecture Example 1		10:11
		Lecture Example 2		12:42
		Additional Example 3		1:15
		Additional Example 4		2:34
IV. Linear Functions and their Graphs
	Slope and Rate of Change			23:58
		Intro		0:00
		Rate of Change		0:27
			Independent Variable	0:37
			Dependent Variable	0:51
		Slope		2:02
			Example	2:19
			Steepness of the Line	4:56
		Possible Slopes		5:58
			Positive	6:13
			Negative	6:34
			Zero	6:50
			Undefined	7:11
		Lecture Example 1		8:03
		Lecture Example 2		10:34
		Additional Example 3		3:50
		Additional Example 4		5:46
	Direct Variation			13:18
		Intro		0:00
		Definitions		0:13
			Direct Variation	0:14
			Constant of Variation	0:26
		Graph		1:02
			Example: Positive and Negative k	1:18
		Applications		1:49
		Lecture Example 1		2:16
		Lecture Example 2		4:39
		Additional Example 3		2:53
		Additional Example 4		4:07
	Slope Intercept Form of an Equation			17:11
		Intro		0:00
		Slope Intercept Form		0:16
			Example	0:37
		Lecture Example 1		2:24
		Lecture Example 2		5:43
		Additional Example 3		2:37
		Additional Example 4		5:29
	Point Slope Form of an Equation			10:32
		Intro		0:00
		Point Slope Form		0:11
			Example	0:50
		Lecture Example 1		2:03
		Lecture Example 2		3:03
		Additional Example 3		2:24
		Additional Example 4		3:07
	Parallel and Perpendicular Lines			18:15
		Intro		0:00
		Parallel Lines		0:12
			Example: Non-vertical Lines	0:32
		Perpendicular lines		1:57
			Example: Slope Product is -1	2:15
			Negative Reciprocal	3:08
		Lecture Example 1		3:58
		Lecture Example 2		7:12
		Additional Example 3		2:58
		Additional Example 4		4:54
V. Systems of Equations
	Graphing Systems of Equations			20:01
		Intro		0:00
		System of Equations		0:09
			Definition	0:15
			Solution	0:59
		Solving by Graphing		1:27
			Example	2:33
		Number of Solutions		3:37
			Independent	3:58
			Dependent	4:03
			Inconsistent	4:08
			Example: 1 Solution	4:15
			Example: No Solution	4:34
			Example: Infinite Solution	4:51
		Lecture Example 1		5:39
		Lecture Example 2		8:51
		Additional Example 3		3:37
		Additional Example 4		3:56
	Solving by Substitution			24:12
		Intro		0:00
		Substitution		0:17
			Example	0:51
		Number of Solutions		1:43
			Infinite Solutions	2:14
			No Solutions	2:50
		Lecture Example 1		3:40
		Lecture Example 2		6:56
		Additional Example 3		6:38
		Additional Example 4		5:18
	Solving by Addition and Subtraction			12:18
		Intro		0:00
		Fundamental Principle		0:18
			Adding or Subtracting	0:50
		Lecture Example 1		1:23
		Lecture Example 2		4:03
		Additional Example 3		2:31
		Additional Example 4		2:21
	Solving by Multiplication			19:11
		Intro		0:00
		Fundamental Principle		0:24
			Multiplication	0:28
		Lecture Example 1		1:40
		Lecture Example 2		6:36
		Additional Example 3		3:50
		Additional Example 4		5:00
	Applications: Systems of Equations			18:24
		Intro		0:00
		Solving Systems of Equations		0:08
			Graphing	0:32
			Addition	0:50
			Subtraction	1:04
			Multiplication	1:13
			Substitution	1:30
		Lecture Example 1		3:20
		Lecture Example 2		4:27
		Additional Example 3		3:54
		Additional Example 4		7:22
VI. Inequalities
	Inequalities: Addition and Subtraction Techniques			10:08
		Intro		0:00
		Fundamental Principle		0:11
		Solutions of Inequalities		0:55
			Inequality	1:02
			Set Builder Notation	1:13
			Example	1:15
			Graph on a Number Line	2:13
		Lecture Example 1		3:29
		Lecture Example 2		5:14
		Additional Example 3		1:39
		Additional Example 4		1:50
	Inequalities: Multiplication and Division Techniques			10:59
		Intro		0:00
		Fundamental Principle		0:11
			Example: Positive Number	0:51
		Fundamental Principle		1:35
			Example: Negative Number	1:50
		Lecture Example 1		4:05
		Lecture Example 2		5:12
		Additional Example 3		1:39
		Additional Example 4		2:49
	Techniques for Multi-Step Inequalities			16:21
		Intro		0:00
		Similarity to Multi-step Equations		0:15
		Inequalities Containing Grouping Symbols		1:03
		Special Cases		1:26
			Solution: All Real Numbers	1:40
			Solution: Empty Set	2:16
		Lecture Example 1		2:54
		Lecture Example 2		4:37
		Additional Example 3		4:03
		Additional Example 4		6:02
	Compound Inequalities			23:00
		Intro		0:00
		Inequalities Combined by 'And'		0:12
			Three Ways to Write Solution Set	1:41
			Set Notation	2:01
			Inequalities	2:12
			Graph	2:29
			Examples	2:31
		Inequalities Combined by 'Or'		4:45
			Example	5:59
		Lecture Example 1		7:40
		Lecture Example 2		10:55
		Additional Example 3		4:04
		Additional Example 4		4:32
	Equations with Absolute Values			23:13
		Intro		0:00
		Absolute Value		0:15
			Example: Distance	1:00
		Absolute Value Function		2:34
			Example	3:05
		Lecture Example 1		4:57
		Lecture Example 2		8:28
		Additional Example 3		4:55
		Additional Example 4		6:34
	Inequalities with Absolute Values			17:34
		Intro		0:00
		Inequalities of the Form \|x\|< n		0:22
		Inequalities of the Form \|x\|> n		3:30
		Lecture Example 1		5:33
		Lecture Example 2		8:50
		Additional Example 3		2:50
		Additional Example 4		3:22
	Graphing Inequalities with Two Variables			30:50
		Intro		0:00
		Graph		0:22
			Half-Plane	0:28
			Boundary	1:37
		Technique for Graphing		3:14
			Example	4:01
			Dashed Line	5:13
			Solid Line	6:30
		Technique for Graphing, cont.		8:58
			Example	9:09
		Lecture Example 1		12:19
		Lecture Example 2		15:48
		Additional Example 3		4:04
		Additional Example 4		6:18
	Graphing Systems of Inequalities			27:38
		Intro		0:00
		System of Inequalities		0:26
			Example	0:43
		Solving a System of Inequalities		1:17
			Example	1:41
		Lecture Example 1		2:58
		Lecture Example 2		7:22
		Additional Example 3		6:31
		Additional Example 4		8:15
VII. Polynomials
	Multiplying Monomials			19:55
		Intro		0:00
		What is a Monomial?		0:43
			Constant	1:11
			Power	1:48
			Exponent and Base	2:39
		Properties of Exponents		3:02
		Simplified Form		5:52
			Each Base Appears Exactly Once	6:02
			No Powers of Powers	6:18
			All Fractions Simplified	6:33
		Lecture Example 1		6:43
		Lecture Example 2		8:12
		Additional Example 3		3:25
		Additional Example 4		6:15
	Dividing Monomials			23:09
		Intro		0:00
		Properties of Exponents		0:26
			Example	1:07
		Properties of Exponents, cont		2:18
			Example	3:18
		Properties of Exponents, cont		4:55
			Example	5:32
		Properties of Exponents, cont		8:49
		Lecture Example 1		11:43
		Lecture Example 2		13:13
		Additional Example 3		3:11
		Additional Example 4		4:22
	Polynomials			16:35
		Intro		0:00
		What is a Polynomial		0:45
			Monomial	0:47
			Example: Trinomial	1:46
			Trinomial	2:10
			Example: Binomial	2:21
			Binomial	2:30
		Degree of a Polynomial		4:28
			Example	4:40
		Ordering Polynomials		6:45
			Example	7:27
		Lecture Example 1		9:27
		Lecture Example 2		10:31
		Additional Example 3		1:41
		Additional Example 4		2:32
	Adding and Subtracting Polynomials			22:00
		Intro		0:00
		Adding Polynomials		0:36
			Like Polynomials	0:48
			Example	1:04
		Subtracting Polynomials		3:55
			Example	4:01
		Lecture Example 1		5:30
		Lecture Example 2		8:04
		Additional Example 3		4:17
		Additional Example 4		7:14
	Multiplying Polynomials by Monomials			24:08
		Intro		0:00
		Distributive Property		0:22
			Basic Principle	0:42
			Example	1:04
		Solving Equations		3:25
		Lecture Example 1		4:26
		Lecture Example 2		7:51
		Additional Example 3		6:31
		Additional Example 4		3:52
	Multiplying Polynomials			26:37
		Intro		0:00
		Distributive Property		0:23
			Example	0:34
			Example	1:55
		Foil Method		5:17
		Lecture Example 1		7:44
		Lecture Example 2		10:15
		Additional Example 3		5:38
		Additional Example 4		6:56
	Special Products			19:40
		Intro		0:00
		Square of a Sum		0:12
			Perfect Square Trinomial	1:43
			Example	2:13
			FOIL Technique	3:09
		Square of a Difference		3:38
			Example	5:27
		Difference of Two Squares		6:12
			Example	7:43
		Lecture Example 1		8:51
		Lecture Example 2		11:06
		Additional Example 3		1:55
		Additional Example 4		4:24
VIII. Factoring
	Factoring Monomials			27:25
		Intro		0:00
		Prime and Composite Numbers		1:01
			Prime Number	1:23
			Composite Number	3:03
		Factored Forms		4:07
			Prime Factored Form	4:19
			Factored Form	5:40
		Greatest Common Factor (GCF)		7:41
			Example	8:00
			GCF of Monomials	10:07
			Example	10:18
		Lecture Example 1		12:52
		Lecture Example 2		17:08
		Additional Example 3		4:01
		Additional Example 4		4:29
	Factoring Using Greatest Common Factor (GCF)			26:03
		Intro		0:00
		Distributive Property		0:19
			Factor Out an Expression	1:21
			Example	2:52
		Factoring by Grouping		4:40
			Example	6:00
		Zero Product Property		8:24
			Example	9:03
		Lecture Example 1		11:19
		Lecture Example 2		14:19
		Additional Example 3		4:16
		Additional Example 4		2:27
	Factoring Trinomials with Leading Coefficient 1			27:37
		Intro		0:00
		Factoring Trinomials		0:23
			Example	2:06
		Rules for Signs		6:27
			Both Positive	6:41
			Both Negative	7:00
			Opposite Signs	7:33
		Solving Equations		8:26
			Example	8:59
		Lecture Example 1		11:14
		Lecture Example 2		14:01
		Additional Example 3		3:56
		Additional Example 4		6:39
	Factoring General Trinomials			34:11
		Intro		0:00
		Factoring Trinomials		0:40
			Example: List	1:38
		Grouping		5:46
			Example	5:55
		Rules for Signs		9:04
			Example	9:22
		Greatest Common Factor (GCF)		10:29
		Prime Polynomials		11:03
			Example	11:32
		Solving Equations		12:32
		Lecture Example 1		13:11
		Lecture Example 2		18:37
		Additional Example 3		3:18
		Additional Example 4		6:25
	Factoring the Difference of Two Squares			20:22
		Intro		0:00
		Difference of Two Squares		0:40
			Example	1:56
		Factoring Using Several Techniques		3:33
		Solving Equations		4:11
		Lecture Example 1		4:55
		Lecture Example 2		6:05
		Additional Example 3		5:21
		Additional Example 4		5:43
	Factoring Perfect Squares			18:07
		Intro		0:00
		Perfect Squares		0:10
			Perfect Square Trinomials	1:17
		Solving Equations		2:53
			Square Root Property	2:58
			Example	3:06
		Lecture Example 1		4:23
		Lecture Example 2		6:56
		Additional Example 3		3:01
		Additional Example 4		4:06
IX. Quadratic Functions
	Graphing Quadratic Functions			28:05
		Intro		0:00
		Parabolas		0:09
		Parabolas That Open Upward		3:58
			Minimum	4:26
		Parabolas That Open Downward		4:54
			Maximum	5:09
		Vertex		7:28
			Example	8:01
		Axis of Symmetry		11:03
		Lecture Example 1		13:27
		Lecture Example 2		17:17
		Additional Example 3		2:07
		Additional Example 4		4:50
	Solving Equations by Graphing			28:18
		Intro		0:00
		Solving a Quadratic Equation		0:22
			Example	0:50
		Two Distinct Solutions/Roots		5:08
		One Double Root		5:58
		No Real Roots		7:14
		Estimating Solutions		8:00
			Example	8:16
			Example	8:31
		Lecture Example 1		9:43
		Lecture Example 2		14:10
		Additional Example 3		4:30
		Additional Example 4		5:19
	Solving Equations by Completing the Square			25:07
		Intro		0:00
		Perfect Square Trinomials		0:22
			Example	1:12
		Completing the Square		3:17
			Example	3:25
		Solving Equations		6:12
			Example	6:27
		Leading Coefficient is 1		8:25
		Lecture Example 1		10:23
		Lecture Example 2		14:17
		Additional Example 3		3:41
		Additional Example 4		4:21
	Solving Equations Using the Quadratic Formula			24:15
		Intro		0:00
		Quadratic Formula		1:26
			Example	2:23
		Discriminant		4:28
			Two Distinct Real Roots	5:07
			One Double Real Root	5:23
			No Real Root	5:42
			Why Does It Work?	6:05
		Lecture Example 1		7:53
		Lecture Example 2		11:50
		Additional Example 3		5:02
		Additional Example 4		2:31
X. Radical Expressions and Equations
	Simplifying Radical Expressions			32:40
		Intro		0:00
		Radical Expressions		0:14
			Radicand	0:28
			Example	0:32
			Simplest Form	1:07
			Example	1:35
		Product Property		2:34
			Verifications	2:47
		Square Roots of Variables with Even Powers		4:27
		Quotient Rule		6:45
			Example	6:55
		Rationalizing Denominators		7:32
			Example	7:41
		Conjugates		10:44
			Examples	10:59
		Simplest Radical Form		14:44
			Example	15:39
		Lecture Example 1		17:34
		Lecture Example 2		19:38
		Additional Example 3		1:55
		Additional Example 4		5:51
	Operations with Radical Expressions			19:59
		Intro		0:00
		Adding and Subtracting Radical Expressions		0:12
			Example	0:19
		Multiplying Radical Expressions		1:53
			Example	2:07
		Lecture Example 1		5:29
		Lecture Example 2		6:36
		Additional Example 3		3:24
		Additional Example 4		6:32
	Solving Radical Equations			26:50
		Intro		0:00
		Radical Equations		0:22
			Example	0:33
		Solving a Radical Equation		2:04
			Example	2:16
		Extraneous Solutions		3:14
			Example	4:31
		Lecture Example 1		7:33
		Lecture Example 2		9:45
		Additional Example 3		5:04
		Additional Example 4		8:09
	Pythagorean Theorem			19:08
		Intro		0:00
		Right Triangles		0:51
			Right Angle	1:03
			Vertex	1:11
			Symbol	1:16
			Hypotenuse and Legs	1:42
		Pythagorean Theorem		2:27
			Example	2:47
			Example	3:12
		Pythagorean Triples		4:03
		Converse of the Pythagorean Theorem		6:39
			Example	7:41
		Lecture Example 1		8:57
		Lecture Example 2		10:05
		Additional Example 3		2:38
		Additional Example 4		3:26
	Distance Formula			18:27
		Intro		0:00
		Distance Formula		0:17
		Missing Coordinates		1:46
			Example	1:55
		Lecture Example 1		4:10
		Lecture Example 2		5:57
		Additional Example 3		3:20
		Additional Example 4		5:10
XI. Rational Expressions and Equations
	Inverse Variation			14:43
		Intro		0:00
		Inverse Variation		0:23
			Constant of Variation	0:37
		Graphing Inverse Variation		1:08
			Example: Hyperbola	1:15
		Product Rule		3:54
		Lecture Example 1		5:31
		Lecture Example 2		7:43
		Additional Example 3		2:02
		Additional Example 4		2:48
	Rational Expressions			32:43
		Intro		0:00
		Rational Expression		0:55
			Example	1:03
		Excluded Values		1:29
			Examples	1:40
		Simplifying Rational Expressions		5:36
			Greatest Common Factor (GCF)	5:46
			Example	5:55
			Example	7:42
		Simplifying and Excluded Values		9:34
		Lecture Example 1		9:50
		Lecture Example 2		13:55
		Additional Example 3		6:07
		Additional Example 4		9:49
	Multiplying Rational Expressions			27:22
		Intro		0:00
		Procedure		0:16
			Example	0:33
		Cancel Before Multiplication		3:44
			Example	3:55
		Rational Expressions Containing Polynomials		6:19
			Example	6:26
		Lecture Example 1		11:09
		Lecture Example 2		15:39
		Additional Example 3		4:09
		Additional Example 4		5:23
	Dividing Rational Expressions			28:30
		Intro		0:00
		Procedure		0:21
			Example	0:59
		Cancel Before Multiplication		4:31
			Example	4:39
		Rational Expressions Containing Polynomials		8:01
			Example	8:08
		Lecture Example 1		10:43
		Lecture Example 2		13:46
		Additional Example 3		4:38
		Additional Example 4		7:17
	Dividing Polynomials			29:44
		Intro		0:00
		Dividing a Polynomial by a Monomial		1:07
			Example	1:14
		Dividing a Polynomial by a Binomial		3:30
			Example	3:51
		Long Division		5:20
			Example	6:25
		Missing Terms		11:11
			Example	12:25
		Lecture Example 1		14:54
		Lecture Example 2		16:35
		Additional Example 3		3:49
		Additional Example 4		6:47
	Adding and Subtracting Rational Expressions with Like Denominators			16:50
		Intro		0:00
		Adding with Like Denominators		0:14
			Example	0:41
		Subtraction with Like Denominators		2:23
			Example	2:30
		Denominators That Are Additive Inverses		2:55
			Example	3:03
		Lecture Example 1		6:41
		Lecture Example 2		7:09
		Additional Example 3		1:13
		Additional Example 4		6:30
	Adding and Subtracting Rational Expressions with Unlike Denominators			36:00
		Intro		0:00
		Least Common Multiple (LCM) of Polynomials		0:34
			Example	0:45
			Example	1:55
		Adding and Subtracting		4:08
			Example	4:45
		Lecture Example 1		8:13
		Lecture Example 2		10:22
		Additional Example 3		8:42
		Additional Example 4		11:40
	Complex Fractions			18:43
		Intro		0:00
		Mixed Expression		0:08
			Example	0:30
		Complex Fraction		2:45
			Example	2:57
			Example	3:11
			Example	3:22
		Simplifying Complex Fractions		3:58
			Why Does It Work?	4:22
		Lecture Example 1		4:48
		Lecture Example 2		8:44
		Additional Example 3		3:33
		Additional Example 4		4:37
	Rational Equations			39:10
		Intro		0:00
		Definition		0:08
			Examples	0:17
		Solving Rational Expressions		3:02
			Example	3:09
		Work Problems		6:31
			Example	6:48
		Extraneous Solutions		13:12
			Example	14:13
		Lecture Example 1		17:21
		Lecture Example 2		19:59
		Additional Example 3		4:13
		Additional Example 4		7:18

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Solving by Multiplication

Solving by Multiplication

Mathematics: Algebra 1

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