Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 9

Putting it All Together

Lesson 4: How Do We Choose?

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topics
Video Transcript: Algebra Nspirations: Inequalities, Part 1 Video Transcript: Algebra Nspirations: Inequalities, 1 Video Transcript: Algebra Nspirations: Inequalities, Part 1

This is the transcript for the video of same title. Video contents: In this Investigation we explore linear inequalities in one variable.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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Inequalities
Video Transcript: Algebra Nspirations: Inequalities, Part 2 Video Transcript: Algebra Nspirations: Inequalities, 2 Video Transcript: Algebra Nspirations: Inequalities, Part 2

This is the transcript for the video of same title. Video contents: In this Investigation we look at linear inequalities in two variables.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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Inequalities
Video Transcript: Algebra Nspirations: Linear Functions Video Transcript: Algebra Nspirations: Linear Functions Video Transcript: Algebra Nspirations: Linear Functions

This is the transcript for the video of same title. Video contents: In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use TI graphing calculators. Examples ranging from air travel, construction, engineering, and space travel provide real-world examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TI-Nspire. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Standard form, slope-intercept form, point-slope form, solving linear equations

Applications of Linear Functions and Graphs of Linear Functions
Video Transcript: Algebra Nspirations: Linear Functions, Part 1 Video Transcript: Algebra Nspirations: Linear Functions, 1 Video Transcript: Algebra Nspirations: Linear Functions, Part 1

This is the transcript for the video of same title. Video contents: In this Investigation we look at linear models for objects moving at a constant speed.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Applications of Linear Functions and Graphs of Linear Functions
Video Transcript: Algebra Nspirations: Linear Functions, Part 2 Video Transcript: Algebra Nspirations: Linear Functions, 2 Video Transcript: Algebra Nspirations: Linear Functions, Part 2

This is the transcript for the video of same title. Video contents: In this Investigation we look at a linear regression for carbon dioxide emission data.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Applications of Linear Functions and Graphs of Linear Functions
Video Transcript: Algebra Nspirations: Logarithms and Logarithmic Functions Video Transcript: Algebra Nspirations: Logarithms Video Transcript: Algebra Nspirations: Logarithms and Logarithmic Functions

This is the transcript for the video of same title. Video contents: This video begins with the historical invention of logarithms that forever changed the world of computation, until the advent of calculators more than 300 years later. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it proceeds to derive the properties of logs, examine logarithmic functions and graphs, and finally explore the well-known Richter logarithmic scale. Concepts explored: functions and inverse functions, logarithms, exponential functions, logarithmic functions

Applications of Exponential and Logarithmic Functions and Graphs of Exponential and Logarithmic Functions
Video Transcript: Algebra Nspirations: Logarithms and Logarithmic Functions, Part 1 Video Transcript: Algebra Nspirations: Logarithms, 1 Video Transcript: Algebra Nspirations: Logarithms and Logarithmic Functions, Part 1

This is the transcript for the video of same title. Video contents: In this Investigation we look at properties of logarithms.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Applications of Exponential and Logarithmic Functions and Graphs of Exponential and Logarithmic Functions
Video Transcript: Algebra Nspirations: Logarithms and Logarithmic Functions, Part 2 Video Transcript: Algebra Nspirations: Logarithms and Logarithmic Functions, 2 Video Transcript: Algebra Nspirations: Logarithms and Logarithmic Functions, Part 2

This is the transcript for the video of same title. Video contents: In this Investigation we look at logarithmic functions and graphs.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Applications of Exponential and Logarithmic Functions and Graphs of Exponential and Logarithmic Functions
Video Transcript: Algebra Nspirations: Quadratic Functions Video Transcript: Algebra Nspirations: Quadratic Functions Video Transcript: Algebra Nspirations: Quadratic Functions

This is the transcript for the video of same title. Video contents: In this program, the TI-Nspire is used to explore the nature of quadratic functions. Examples ranging from space travel and projectile motion provide real-world examples for discovering algebraic concepts. All examples are solved graphically. The teacher's guide provides all keystrokes shown in the video, as well as providing support for TI-84 users. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Quadratic functions and equations, standard form, graphing quadratic equations, solving quadratic equations graphically

Applications of Quadratic Functions, Graphs of Quadratic Functions and Quadratic Equations and Functions
Video Transcript: Algebra Nspirations: Quadratic Functions, Part 1 Video Transcript: Algebra Nspirations: Quadratic Functions, 1 Video Transcript: Algebra Nspirations: Quadratic Functions, Part 1

This is the transcript for the video of same title. Video contents: In this Investigation we explore quadratic functions and their graphs.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Applications of Quadratic Functions, Graphs of Quadratic Functions and Quadratic Equations and Functions
Video Transcript: Algebra Nspirations: Quadratic Functions, Part 2 Video Transcript: Algebra Nspirations: Quadratic Functions, 2 Video Transcript: Algebra Nspirations: Quadratic Functions, Part 2

This is the transcript for the video of same title. Video contents: In this Investigation we use a quadratic model to explore the path of a rocket into space.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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Applications of Quadratic Functions, Graphs of Quadratic Functions and Quadratic Equations and Functions
Video Transcript: Algebra Nspirations: Rational Functions and Expressions Video Transcript: Algebra Nspirations: Rational Functions and Expressions Video Transcript: Algebra Nspirations: Rational Functions and Expressions

This is the transcript for the video of same title. Video contents: After briefly reviewing the concept of inverse variation, this video explores Boyle??s law, a real world example of an inversely proportional relationship between pressure and volume of a gas. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it goes on to examine similarities and differences among rational functions and numbers. Finally, it takes a look at rational functions graphs and ends with a delightful example merging Euclidean and analytic geometry, thanks to the TI-Nspire technology. Concepts explored: functions, rational expressions, rational functions, asymptotes

Rational Expressions and Rational Functions and Equations
Video Transcript: Algebra Nspirations: Rational Functions and Expressions, Part 1 Video Transcript: Algebra Nspirations: Rational Functions and Expressions, 1 Video Transcript: Algebra Nspirations: Rational Functions and Expressions, Part 1

This is the transcript for the video of same title. Video contents: In this Investigation we look at an application of rational functions: Boyle's Law.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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Rational Expressions and Rational Functions and Equations
Video Transcript: Algebra Nspirations: Rational Functions and Expressions, Part 2 Video Transcript: Algebra Nspirations: Rational Functions and Expressions, 2 Video Transcript: Algebra Nspirations: Rational Functions and Expressions, Part 2

This is the transcript for the video of same title. Video contents: In this Investigation we look at graphs of rational functions.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Rational Expressions and Rational Functions and Equations
Video Transcript: Algebra Nspirations: Solving Systems of Equations Video Transcript: Algebra Nspirations: Solving Systems of Equations Video Transcript: Algebra Nspirations: Solving Systems of Equations

This is the transcript for the video of same title. Video contents: Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video introduces students to systems of linear equations in two or three unknowns. To solve these systems, the host illustrates a variety of methods: four involve the TI-Nspire (spreadsheet, graphs and geometry, matrices and nSolve) and two are the classic algebraic methods known as substitution and elimination, also called the linear combinations method. The video ends with a summary of the three possible types of solutions. Concepts explored: equations, linear equations, linear systems

Applications of Linear Systems, Matrix Operations and Solving Systems of Equations
Video Transcript: Algebra Nspirations: Solving Systems of Equations, Part 1 Video Transcript: Algebra Nspirations: Solving Systems of Equations, 1 Video Transcript: Algebra Nspirations: Solving Systems of Equations, Part 1

This is the transcript for the video of same title. Video contents: In this Investigation we solve a linear system.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Applications of Linear Systems, Matrix Operations and Solving Systems of Equations
Video Transcript: Algebra Nspirations: Solving Systems of Equations, Part 2 Video Transcript: Algebra Nspirations: Solving Systems of Equations, 2 Video Transcript: Algebra Nspirations: Solving Systems of Equations, Part 2

This is the transcript for the video of same title. Video contents: In this Investigation we use matrices and the elimination method to solve a linear system.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Applications of Linear Systems, Matrix Operations and Solving Systems of Equations
Video Transcript: Algebra Nspirations: Variables and Equations, Part 1 Video Transcript: Algebra Nspirations: Variables and Equations, 1 Video Transcript: Algebra Nspirations: Variables and Equations, Part 1

This is the transcript for the video of same title. Video contents: In this Investigation we get a historical overview of equations.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Applications of Equations and Inequalities
Video Transcript: Algebra Nspirations: Variables and Equations, Part 2 Video Transcript: Algebra Nspirations: Variables and Equations, 2 Video Transcript: Algebra Nspirations: Variables and Equations, Part 2

This is the transcript for the video of same title. Video contents: In this Investigation we solve linear and quadratic equations.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Applications of Equations and Inequalities
Video Transcript: Geometry Applications: Area and Volume, Segment 3: Ratio of Surface Area to Volume Video Transcript: Geometry Applications: Area and Volume, Segment 3: Ratio of Surface Area to Volume Video Transcript: Geometry Applications: Area and Volume, Segment 3: Ratio of Surface Area to Volume

This is the transcript for the video of same title. Video contents: The Citibank Tower in New York City presents some unique design challenges. In addition it has to cope with a problem that all tall structure have to deal with: heat loss. By managing the ratio of surface area to volume, a skyscraper can effective manage heat loss.

Applications of Surface Area and Volume
Video Transcript: Algebra Nspirations: Variables and Equations Video Transcript: Algebra Nspirations: Variables and Equations Video Transcript: Algebra Nspirations: Variables and Equations

This is the transcript for the video of same title. Video contents: Ever since the mathematics of the Babylonians, equations have played a central role in the development of algebra. Written and hosted by internationally acclaimed mathematics educator Dr. Monica Neagoy, this video traces the history and evolution of equations. It explores the two principal equations encountered in an introductory algebra course -- linear and quadratic -- in an engaging way. The foundations of algebra are explored and fundamental questions about the nature of algebra are answered. In addition, problems involving linear and quadratic equations are solved using the TI-Nspire graphing calculator. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series.

Applications of Equations and Inequalities
Math Example--Rational Concepts--Rational Expressions: Example 1 Math Example--Rational Concepts--Rational Expressions: Example 1 Math Example--Rational Concepts--Rational Expressions: Example 1

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/2 + 1/3. The solution involves finding a common denominator, which is 6, and then adding the fractions to get 5/6. To solve this, we multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 3/3) + (1 * 2/2) = 3/6 + 2/6. Then, we add the numerators while keeping the common denominator: (3 + 2)/6 = 5/6.

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 2 Math Example--Rational Concepts--Rational Expressions: Example 2 Math Example--Rational Concepts--Rational Expressions: Example 2

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/4 - 1/5. The solution involves finding a common denominator, which is 20, and then subtracting the fractions to get 1/20. We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 5/5) - (1 * 4/4) = 5/20 - 4/20. Then, we subtract the numerators while keeping the common denominator: (5 - 4)/20 = 1/20.

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 3 Math Example--Rational Concepts--Rational Expressions: Example 3 Math Example--Rational Concepts--Rational Expressions: Example 3

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/x + 1/3. The solution involves finding a common denominator, which is 3x, and then adding the fractions to get (x + 3)/3x. We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 3/3) + (1 * x/x) = 3/(3x) + x/(3x). Then, we add the numerators while keeping the common denominator: (3 + x)/(3x) = (x + 3)/(3x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 4 Math Example--Rational Concepts--Rational Expressions: Example 4 Math Example--Rational Concepts--Rational Expressions: Example 4

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/x - 1/2. The solution involves finding a common denominator, which is 2x, and then subtracting the fractions to get (x - 2)/2x. We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 2/2) - (1 * x/x) = 2/(2x) - x/(2x). Then, we subtract the numerators while keeping the common denominator: (2 - x)/(2x) = (x - 2)/(2x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 5 Math Example--Rational Concepts--Rational Expressions: Example 5 Math Example--Rational Concepts--Rational Expressions: Example 5

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/(2x) + 1/5. The solution involves finding a common denominator, which is 10x, and then adding the fractions to get (2x + 5)/(10x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * 5)/(2x * 5) + (1 * 2x)/(5 * 2x) = 5/(10x) + 2x/(10x). Then, we add the numerators while keeping the common denominator: (5 + 2x)/(10x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 6 Math Example--Rational Concepts--Rational Expressions: Example 6 Math Example--Rational Concepts--Rational Expressions: Example 6

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/(4x) - 1/7. The solution involves finding a common denominator, which is 28x, and then subtracting the fractions to get (7 - 4x)/(28x), which simplifies to (4x - 7)/(28x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * 7)/(4x * 7) - (1 * 4x)/(7 * 4x) = 7/(28x) - 4x/(28x). Then, we subtract the numerators while keeping the common denominator: (7 - 4x)/(28x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 7 Math Example--Rational Concepts--Rational Expressions: Example 7 Math Example--Rational Concepts--Rational Expressions: Example 7

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/(8x) + 1/8. The solution involves finding a common denominator, which is 8x, and then adding the fractions to get (x + 1)/(8x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * x)/(8x * x) + (1 * x)/(8 * x) = 1/(8x) + x/(8x). Then, we add the numerators while keeping the common denominator: (1 + x)/(8x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 8 Math Example--Rational Concepts--Rational Expressions: Example 8 Math Example--Rational Concepts--Rational Expressions: Example 8

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/(9x) - 1/3. The solution involves finding a common denominator, which is 9x, and then subtracting the fractions to get (1 - 3x)/(9x), which simplifies to (3x - 1)/(9x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * x)/(9x * x) - (3 * x)/(3 * x) = 1/(9x) - 3x/(9x). Then, we subtract the numerators while keeping the common denominator: (1 - 3x)/(9x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 9 Math Example--Rational Concepts--Rational Expressions: Example 9 Math Example--Rational Concepts--Rational Expressions: Example 9

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/(2x) + 1/(5x). The solution involves finding a common denominator, which is 10x, and then adding the fractions to get 7/(10x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * 5)/(2x * 5) + (1 * 2)/(5x * 2) = 5/(10x) + 2/(10x). Then, we add the numerators while keeping the common denominator: (5 + 2)/(10x) = 7/(10x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 10 Math Example--Rational Concepts--Rational Expressions: Example 10 Math Example--Rational Concepts--Rational Expressions: Example 10

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/(8x) - 1/(3x). The solution involves finding a common denominator, which is 24x, and then subtracting the fractions to get -5/(24x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * 3)/(8x * 3) - (1 * 8)/(3x * 8) = 3/(24x) - 8/(24x). Then, we subtract the numerators while keeping the common denominator: (3 - 8)/(24x) = -5/(24x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 11 Math Example--Rational Concepts--Rational Expressions: Example 11 Math Example--Rational Concepts--Rational Expressions: Example 11

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 2/(3x) + 4/(5x). The solution involves finding a common denominator, which is 15x, and then adding the fractions to get 22/(15x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (2 * 5)/(3x * 5) + (4 * 3)/(5x * 3) = 10/(15x) + 12/(15x). Then, we add the numerators while keeping the common denominator: (10 + 12)/(15x) = 22/(15x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 12 Math Example--Rational Concepts--Rational Expressions: Example 12 Math Example--Rational Concepts--Rational Expressions: Example 12

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 4/(7x) - 3/(8x). The solution involves finding a common denominator, which is 56x, and then subtracting the fractions to get 11/(56x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (4 * 8)/(7x * 8) - (3 * 7)/(8x * 7) = 32/(56x) - 21/(56x). Then, we subtract the numerators while keeping the common denominator: (32 - 21)/(56x) = 11/(56x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 13 Math Example--Rational Concepts--Rational Expressions: Example 13 Math Example--Rational Concepts--Rational Expressions: Example 13

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/(x + 1) + 1/3. The solution involves finding a common denominator, which is 3(x + 1), and then adding the fractions to get (x + 4)/(3(x + 1)). We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 3)/(x + 1) * 3 + (1 * (x + 1))/(3 * (x + 1)) = 3/(3(x + 1)) + (x + 1)/(3(x + 1)). Then, we add the numerators while keeping the common denominator: (3 + x + 1)/(3(x + 1)) = (x + 4)/(3(x + 1)).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 14 Math Example--Rational Concepts--Rational Expressions: Example 14 Math Example--Rational Concepts--Rational Expressions: Example 14

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/(x + 3) - 1/4. The solution involves finding a common denominator, which is 4(x + 3), and then subtracting the fractions to get (-x + 1)/(4(x + 3)). We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 4)/(x + 3) * 4 - (1 * (x + 3))/(4 * (x + 3)) = 4/(4(x + 3)) - (x + 3)/(4(x + 3)). Then, we subtract the numerators while keeping the common denominator: (4 - (x + 3))/(4(x + 3)) = (-x + 1)/(4(x + 3)).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 15 Math Example--Rational Concepts--Rational Expressions: Example 15 Math Example--Rational Concepts--Rational Expressions: Example 15

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1 / (x - 5) + 1 / 6. The solution involves finding a common denominator, which is 6(x - 5), and then adding the fractions to get (x + 1) / (6(x - 5)). We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 6) / ((x - 5) * 6) + (1 * (x - 5)) / (6 * (x - 5)) = 6 / (6(x - 5)) + (x - 5) / (6(x - 5)). Then, we add the numerators while keeping the common denominator: (6 + x - 5) / (6(x - 5)) = (x + 1) / (6(x - 5)).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 16 Math Example--Rational Concepts--Rational Expressions: Example 16 Math Example--Rational Concepts--Rational Expressions: Example 16

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1 / (x - 7) + 1 / 8. The solution involves finding a common denominator, which is 8(x - 7), and then adding the fractions to get (x + 1) / (8(x - 7)). We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 8) / ((x - 7) * 8) + (1 * (x - 7)) / (8 * (x - 7)) = 8 / (8(x - 7)) + (x - 7) / (8(x - 7)). Then, we add the numerators while keeping the common denominator: (8 + x - 7) / (8(x - 7)) = (x + 1) / (8(x - 7)).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 17 Math Example--Rational Concepts--Rational Expressions: Example 17 Math Example--Rational Concepts--Rational Expressions: Example 17

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1 / (x - 9) - 1 / 10. The solution involves finding a common denominator, which is 10(x - 9), and then subtracting the fractions to get (-x + 19) / (10(x - 9)). We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 10) / ((x - 9) * 10) - (1 * (x - 9)) / (10 * (x - 9)) = 10 / (10(x - 9)) - (x - 9) / (10(x - 9)). Then, we subtract the numerators while keeping the common denominator: (10 - (x - 9)) / (10(x - 9)) = (19 - x) / (10(x - 9)) = (-x + 19) / (10(x - 9)).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 18 Math Example--Rational Concepts--Rational Expressions: Example 18 Math Example--Rational Concepts--Rational Expressions: Example 18

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 19 Math Example--Rational Concepts--Rational Expressions: Example 19 Math Example--Rational Concepts--Rational Expressions: Example 19

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 20 Math Example--Rational Concepts--Rational Expressions: Example 20 Math Example--Rational Concepts--Rational Expressions: Example 20

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 21 Math Example--Rational Concepts--Rational Expressions: Example 21 Math Example--Rational Concepts--Rational Expressions: Example 21

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 22 Math Example--Rational Concepts--Rational Expressions: Example 22 Math Example--Rational Concepts--Rational Expressions: Example 22

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 23 Math Example--Rational Concepts--Rational Expressions: Example 23 Math Example--Rational Concepts--Rational Expressions: Example 23

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 24 Math Example--Rational Concepts--Rational Expressions: Example 24 Math Example--Rational Concepts--Rational Expressions: Example 24

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 25 Math Example--Rational Concepts--Rational Expressions: Example 25 Math Example--Rational Concepts--Rational Expressions: Example 25

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 26 Math Example--Rational Concepts--Rational Expressions: Example 26 Math Example--Rational Concepts--Rational Expressions: Example 26

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 27 Math Example--Rational Concepts--Rational Expressions: Example 27 Math Example--Rational Concepts--Rational Expressions: Example 27

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 28 Math Example--Rational Concepts--Rational Expressions: Example 28 Math Example--Rational Concepts--Rational Expressions: Example 28

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 1 Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 1 Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 1

Topic

Rational Functions

Description

This math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / x. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph is a hyperbola with branches in the first and third quadrants, illustrating the characteristic shape of this basic rational function.

Rational Functions and Equations