Unit 1: Solving Compound Inequalities, Absolute Value Inequalities, and Systems of Equations In this unit, you will study how to solve more complicated linear equations, such as linear equations that include conjunctions and absolute values. Then, you will study techniques of solving a system of linear equations. Lastly, applications of all types of linear equations are presented, such as distance, rate, and time problems; gravitational pull problems; and other interesting real-world problems.
Unit 1 Time Advisory
Completing this unit should take approximately 28 hours.
☐ Subunit 1.1: 4.5 hours
☐ Subunit 1.2: 4.5 hours
☐ Subunit 1.3: 5 hours
☐ Subunit 1.4: 4 hours
☐ Subunit 1.5: 6 hours
☐ Subunit 1.6: 4 hours
Unit1 Learning Outcomes
Upon successful completion of this unit, you will be able to:
- solve, graph, and give interval notation for compound inequalities;
- solve, graph, and give interval notation for absolute value
inequalities;
- solve systems of linear equations with two or three variables using
substitution and elimination (may have infinite or no solution); and
- solve applications of linear systems, including mixture problems,
value problems, and interest problems.
1.1 Compound Inequalities
- Reading: Washington State Board for Community and Technical
Colleges: Tyler Wallace’s Beginning Algebra and Intermediate
Algebra, 2nd Edition: “Chapter 3, Section 3.1: Solve and Graph
Inequalities” and “Chapter 3, Section 3.2: Compound Inequalities”
Link: Washington State Board for Community and Technical Colleges:
Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd
Edition: “Chapter 3, Section 3.1: Solve and Graph
Inequalities”
(PDF) and “Chapter 3, Section 3.2: Compound
Inequalities” (PDF)
Instructions: Read Sections 3.1 and 3.2 in Chapter 3 of this
textbook, pages 118–127, to learn about solving and graphing
inequalities. In particular, the AND and OR operators are
introduced, which are necessary for the absolute value inequalities
you will study in Subunit 1.2. Note that this reading also covers
the topics in Subunits 1.1.1–1.1.3.
Reading these sections and taking notes should take approximately 2
hours.
Terms of Use: This resource is licensed under a Creative Commons
Attribution 3.0 Unported
License. It is
attributed to Tyler Wallace and the original version can be found
here.
- Assessment: Big Bend Community College: Tyler Wallace’s
Intermediate Algebra Lab Notebook: “Compound Inequalities”
Link: Big Bend Community College: Tyler Wallace’s Intermediate
Algebra Lab Notebook: “Compound
Inequalities”
(PDF)
Instructions: Complete pages 4–6 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 1.1.1–1.1.3, and then review the worksheet as you follow along with the videos for solutions.
Completing this assessment should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.
1.1.1 The AND Operator Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.1.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Compound
Inequalities – AND”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Compound
Inequalities – AND”
(YouTube)
Instructions: Watch the video linked above, which discusses the compound inequality AND. The AND operator corresponds to the English conjunction and. For instance, “I am going to town, and I am going to the movies.” This statement is true if I complete both, I go to town and I go to the movies.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.1.2 The OR Operator Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.1.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Compound
Inequalities – OR”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Compound
Inequalities – OR”
(YouTube)
Instructions: Watch the video linked above, which discusses the compound inequality OR. Note the difference between the operators AND and OR and relate them to how you use the English grammar conjunctions and and or.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.1.3 Tripartite Compound Inequalities
Note: This subunit is also covered by the reading and assessment
assigned in Subunit 1.1.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Compound
Inequalities – Tripartite”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Compound
Inequalities –
Tripartite” (YouTube)
Instructions: Watch the video linked above, which discusses tripartite compound inequality – inequality with three parts, usually with one part being the AND operator.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.2 Absolute Value Inequalities
- Reading: Washington State Board for Community and Technical
Colleges: Tyler Wallace’s Beginning Algebra and Intermediate
Algebra, 2nd Edition: “Chapter 3, Section 3.3: Absolute Value
Inequalities”
Link: Washington State Board for Community and Technical Colleges:
Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd
Edition: “Chapter 3, Section 3.3: Absolute Value
Inequalities” (PDF)
Instructions: Read Section 3.3 in Chapter 3 of your textbook, pages
128–132, to learn about solving absolute value inequalities. Notice
how absolute value inequalities are related to compound
inequalities. This reading also covers the topics in Subunits
1.2.1–1.2.3.
Reading this section and taking notes should take approximately 2
hours.
Terms of Use: This resource is licensed under a Creative Commons
Attribution 3.0 Unported
License. It is
attributed to Tyler Wallace and the original version can be found
here.
- Assessment: Big Bend Community College: Tyler Wallace’s
Intermediate Algebra Lab Notebook: “Absolute Value Inequalities”
Link: Big Bend Community College: Tyler Wallace’s Intermediate
Algebra Lab Notebook: “Absolute Value
Inequalities”
(PDF)
Instructions: Complete pages 7–9 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 1.2.1–1.2.3, and then review the worksheet as you follow along with the videos for solutions.
Completing this assessment should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.
1.2.1 Simple Absolute Value Inequalities Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.2.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Absolute
Value Inequality – Simple”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Absolute Value
Inequality – Simple”
(YouTube)
Instructions: Watch the video linked above, which discusses absolute value inequalities. In some cases, absolute value inequalities are a simpler way of expressing compound inequalities.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.2.2 Solving Absolute Value Inequalities Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.2.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Absolute
Value Inequality – Solving"
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Absolute Value
Inequality – Solving”
(YouTube)
Instructions: Watch the video linked above, which discusses absolute value inequalities. As noted above, sometimes absolute value inequalities are a simpler and more meaningful way of expressing compound inequalities using AND and/or OR. This video shows the absolute value of an algebraic expression of more than one term.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.2.3 Isolating the Absolute Value Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.2.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Absolute
Value Inequality – Isolate Absolute”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Absolute Value
Inequality – Isolate
Absolute” (YouTube)
Instructions: Watch the video linked above, which discusses absolute value inequalities in which an absolute value expression is embedded into another algebraic expression in an inequality. It is important to note that the absolute value expression must be isolated on one side of the inequality before expressing the inequality without the absolute value sign.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.3 Systems of Equations - Reading: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 4, Section 4.1: Graphing”, “Chapter 4, Section 4.2: Substitution”, “Chapter 4, Section 4.3: Addition/Elimination” Link: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition:
- [“Chapter 4, Section 4.1:
Graphing”](http://www.saylor.org/site/wp-content/uploads/2011/12/SAYLOR-MA001-TEXT.pdf)
(PDF)
- [“Chapter 4, Section 4.2:
Substitution”](http://www.saylor.org/site/wp-content/uploads/2011/12/SAYLOR-MA001-TEXT.pdf)
(PDF)
- [“Chapter 4, Section 4.3:
Addition/Elimination”](http://www.saylor.org/site/wp-content/uploads/2011/12/SAYLOR-MA001-TEXT.pdf)
(PDF)
Instructions: Read Sections 4.1–4.3 in Chapter 4 of your textbook,
pages 134–150, to learn about solving systems of linear equations.
Systems of linear equations are used with applications that require
two or more unknowns and have two or more relationships between the
unknowns. Note that this reading also covers all the topics under
Subunits 1.3.1–1.3.8.
Reading this section and taking notes should take approximately 2
hours.
Terms of Use: This resource is licensed under a [Creative Commons
Attribution 3.0 Unported
License](http://creativecommons.org/licenses/by/3.0/). It is
attributed to Tyler Wallace and the original version can be found
[here](http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf).
- Assessment: Big Bend Community College: Tyler Wallace’s
Intermediate Algebra Lab Notebook: “Systems of Equations”
Link: Big Bend Community College: Tyler Wallace’s Intermediate
Algebra Lab Notebook: “Systems of
Equations”
(PDF)
Instructions: Complete pages 10–17 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 1.3.1–1.3.8, and then review the worksheet as you follow along with the videos for solutions.
Completing this assessment should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.
1.3.1 Substitution Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.3.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Introduction to Substitution”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Introduction to
Substitution”
(YouTube)
Instructions: Watch the video linked above, which discusses examples of systems of equations in which one of the equations is a simple equality like x = 3, and the second equation is a relationship like x + y = 6. Now you need to solve for y.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.3.2 Substitute Expression Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.3.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Substitute Expression”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Substitute
Expression” (YouTube)
Instructions: Watch the video linked above, which discusses systems of equations in which both equations are relationships between two variables. In this instance, one of the variables in one of the equations equals an algebraic expression of the other variable. You can then plug the algebraic expression into the other equation, which will produce one equation with one unknown that can be solved using previously learned techniques. Once the second variable is known, you can use substitution to solve for the first variable.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.3.3 Solve for a Variable Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.3.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Solve for a Variable”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Solve for a
Variable” (YouTube)
Instructions: Watch the video linked above, which continues our discussion on systems of equations and shows examples of solving for a variable in one of the equations and then substituting the solution in the other equation. This video extends the techniques you studied in Subunit 1.3.2.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.3.4 Special Cases with Substitution Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.3.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Special Cases with Substitution”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Special Cases with
Substitution”
(YouTube)
Instructions: Watch the video linked above, which discusses solutions to systems of equations. There are three possibilities: a unique solution, no solution, and an infinite number of solutions. This video describes how you can determine which of the three cases exist for a system of equations.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.3.5 Add Equations Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.3.
Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of Equations – Addition” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of Equations – Addition” (YouTube)
Instructions: Watch the video linked above, which discusses the addition technique for solving a system of equations. The addition method is when you can add the two equations and one of the variables will be eliminated. If the coefficients of one of the variables are opposite in signs, then adding the equations will result in one equation with one variable.You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.3.6 Multiply One Equation Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.3.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Multiply and Add”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Multiply and
Add” (YouTube)
Instructions: Watch the video linked above, which discusses the multiply and add technique for solving a system of equations. If the coefficient of one of the variables is different, you may be able to multiply one of the equations by an appropriate constant that will result in the coefficient being the same but opposite in signs.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.3.7 Multiply Both Equations Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.3.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Multiplying Two Equations”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Multiplying Two
Equations” (YouTube)
Instructions: Watch the video linked above, which discusses solving a system of equations by multiplying two different equations by a number and then adding the equations. This video has examples extending the previous lesson. Here you multiply each equation by an appropriate constant to make one of the variable’s coefficients opposite in sign.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.3.8 Special Cases with Elimination/Addition Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.3.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Special Cases with Addition”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
Equations – Special Cases with
Addition” (YouTube)
Instructions: Watch the video linked above, which discusses the two special cases when solving a system of equations by addition: when the system reduces to an identity (such as 2 = 2) or the system reduces to an absurdity (such as 0 = 8).
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.4 Three Variables
- Reading: Washington State Board for Community and Technical
Colleges: Tyler Wallace’s Beginning Algebra and Intermediate
Algebra, 2nd Edition: “Chapter 4, Section 4.4: Three Variables”
Link: Washington State Board for Community and Technical Colleges:
Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd
Edition: “Chapter 4, Section 4.4: Three
Variables”
(PDF)
Instructions: Read Section 4.4 in Chapter 4 of your textbook, pages
151–157, to learn about solving systems of linear equations with
three variables. The techniques learned for solving two equations
with two unknowns are extended to solving three equations with three
unknowns. This material also covers Subunits 1.4.1–1.4.4.
Reading this section and taking notes should take approximately 2
hours.
Terms of Use: This resource is licensed under a Creative Commons
Attribution 3.0 Unported
License. It is
attributed to Tyler Wallace and the original version can be found
here.
- Assessment: Big Bend Community College: Tyler Wallace’s
Intermediate Algebra Lab Notebook: “3 Variables”
Link: Big Bend Community College: Tyler Wallace’s Intermediate
Algebra Lab Notebook: “3
Variables”
(PDF)
Instructions: Complete pages 18–19 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 1.4.1–1.4.4, and then review the worksheet as you follow along with the videos for solutions.
Completing this assessment should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.
1.4.1 System of Three Equations, Three Unknowns – The Simple Case (Part 1) Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.4.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
3 Variables – Simple (Part 1)”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of 3
Variables – Simple (Part
1)” (YouTube)
Instructions: Watch the video linked above, which discusses solving a system of three equations with three unknowns. Here, you consider two equations at a time and use the previous lessons on eliminating one of the variables. By using this technique, you will be able to reduce the system to two equations and two unknowns.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.4.2 System of Three Equations, Three Unknowns – The Simple Case (Part 2) Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.4.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
3 Variables – Simple (Part 2)”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of 3
Variables – Simple (Part
2)” (YouTube)
Instructions: Watch the video linked above, which discusses solving a system of three equations with three unknowns. This video is a continuation of the previous lesson. It completes the problem by showing how to solve for z, and then gives another example.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.4.3 Systems of Three Variables Requiring Multiplication (Part 1) Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.4.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
3 Variables – Multiplying to Eliminate (Part 1)”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of 3
Variables – Multiplying to Eliminate (Part
1)” (YouTube)
Instructions: Watch the video linked above, which discusses solving a system of three equations with three unknowns by multiplying each equation by an appropriate constant and adding the resulting equations (two at a time). You will reduce three equations down to two equations with two unknowns. You can then apply previously learned techniques to solve.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.4.4 Systems of Three Variables Requiring Multiplication (Part 2) Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.4.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of
3 Variables – Multiplying to Eliminate (Part 2)”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Systems of 3
Variables – Multiplying to Eliminate (Part
2)” (YouTube)
Instructions: Watch the video linked above, which discusses how to finish solving for the three variables by using a technique referred to as back-substitution. This is the completion of the previous video’s example.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.5 Value/Interest Problems
- Reading: Washington State Board for Community and Technical
Colleges: Tyler Wallace’s Beginning Algebra and Intermediate
Algebra, 2nd Edition: “Chapter 4, Section 4.5: Application: Value
Problems”
Link: Washington State Board for Community and Technical Colleges:
Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd
Edition: “Chapter 4, Section 4.5: Application: Value
Problems”
(PDF)
Instructions: Read Section 4.5 in Chapter 4 of your textbook, pages
158–166, to learn about several applications of systems of linear
equations. One of these applications, known as value problems,
determines the distribution of coins or tickets. Another, known as
interest problems, helps determine the distribution of several
investments if the total return on the investments is known. Note
that this reading covers the topics in Subunits 1.5.1–1.5.6.
Reading this section and taking notes should take approximately 2
hours.
Terms of Use: This resource is licensed under a Creative Commons
Attribution 3.0 Unported
License. It is
attributed to Tyler Wallace and the original version can be found
here.
- Assessment: Big Bend Community College: Tyler Wallace’s
Intermediate Algebra Lab Notebook: “Value/Interest Problems”
Link: Big Bend Community College: Tyler Wallace’s Intermediate
Algebra Lab Notebook: “Value/Interest
Problems”
(PDF)
Instructions: Complete pages 20–23 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 1.5.1–1.5.6, and then review the worksheet as you follow along with the videos for solutions.
Completing this assessment should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.
1.5.1 Value Problems with One Variable Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.5.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series:
“Value/Interest – Value with 1 Variable"
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Value/Interest
– Value with 1
Variable” (YouTube)
Instructions: Watch the video linked above, which discusses the value application with one variable. Suppose you have twice as many dimes as quarters and the total amount of money is $4.95, how many dimes and quarters do you have?
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.5.2 Interest Problems with One Variable Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.5.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series:
“Value/Interest – Interest with 1 Variable”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Value/Interest
– Interest with 1
Variable” (YouTube)
Instructions: Watch the video linked above, which discusses the interest application with one variable, such as the following: I invested $1900 and $1500 in two different CD accounts with the second CD paying 3% more than the first CD. If my total return is $113, how much was the rate on each CD?
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.5.3 Value Problems with Two Variables (Part 1) Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.5.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series:
“Value/Interest – Value with 2 Variables (Part 1)”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Value/Interest
– Value with 2 Variables (Part
1)” (YouTube)
Instructions: Watch the video linked above, which discusses the value application using two variables and two equations. For example, suppose you have $2.15 consisting of quarters and dimes, and you have a total of 11 coins. How many of each coin do you have?
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.5.4 Value Problems with Two Variables (Part 2) Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.5.
Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Value/Interest – Value with 2 Variables (Part 2)” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Value/Interest – Value with 2 Variables (Part 2)” (YouTube)
Instructions: Watch the video linked above, which discusses another value application of two equations and two unknowns. For example, suppose you are in charge of a charity concert and you charge $2.50 for adults and $1.75 for children. The total collected was $228.00 and 105 people attended. How many children and how many adults attended?
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.5.5 Interest Problems with Two Variables (Part 1) Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.5.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series:
“Value/Interest – Interest with 2 Variables (Part 1)”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Value/Interest
– Interest with 2 Variables (Part
1)” (YouTube)
Instructions: Watch the video linked above, which discusses the interest application with two variables. Again dealing with investments as above, but this time you are unsure how much is in each account, and you know only the rate of return of each account, the total invested, and the total return.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.5.6 Interest Problems with Two Variables (Part 2)
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series:
“Value/Interest – Interest with 2 Variables (Part 2)”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Value/Interest
– Interest with 2 Variables (Part
2)” (YouTube)
Instructions: Watch the video linked above, which discusses the
interest application with two variables. This application is similar
to the application discussed above except instead of investments
this application is dealing with a loan.
You may watch the video as often as you please. You may refer to
the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take
approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
1.6 Mixture Problems
- Reading: Washington State Board for Community and Technical
Colleges: Tyler Wallace’s Beginning Algebra and Intermediate
Algebra, 2nd Edition: “Chapter 4, Section 4.6: Application: Mixture
Problems”
Link: Washington State Board for Community and Technical Colleges:
Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd
Edition: “Chapter 4, Section 4.6: Application: Mixture
Problems”
(PDF)
Instructions: Read Section 4.6 in Chapter 4 of your textbook, pages
167–174, to learn about more applications of systems of linear
equations – in particular, applications dealing with mixture. This
application is important in chemistry and many real-world
situations. As an example, suppose you need 1425 mL of 10% alcohol
solution. On hand you have a 5% alcohol mixture and pure alcohol.
How much of each should you use? This material also covers Subunits
1.6.1–1.6.4.
Reading this section and taking notes should take approximately 2
hours.
Terms of Use: This resource is licensed under a Creative Commons
Attribution 3.0 Unported
License. It is
attributed to Tyler Wallace and the original version can be found
here.
- Assessment: Big Bend Community College: Tyler Wallace’s
Intermediate Algebra Lab Notebook: “Mixture Problems”
Link: Big Bend Community College: Tyler Wallace’s Intermediate
Algebra Lab Notebook: “Mixture
Problems”
(PDF)
Instructions: Complete pages 24–26 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 1.6.1–1.6.4, and then review the worksheet as you follow along with the videos for solutions.
Completing this assessment should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.
1.6.1 Mixture Problems with a Known Starting Amount Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.6.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Mixture
Problems – Known Starting Amount”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Mixture
Problems – Known Starting
Amount” (YouTube)
Instructions: Watch the video linked above, which discusses the mixture application when you know a starting amount. As an example, a store owner wants to make a mixture of chocolate and nuts that will be sold for $4.33 a pound. He has 25 pounds of nuts that cost $2.50 a pound. How many pounds of chocolate must be added if the chocolate sells for $8.50 a pound?
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.6.2 Mixture Problems with an Unknown Starting Amount (Part 1) Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.6.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Mixture
Problems – Unknown Starting Amount (Part 1)”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Mixture
Problems – Unknown Starting Amount (Part
1)” (YouTube)
Instructions: Watch the video linked above, which discusses a mixture application where the ending result is known. As an example, a chemist needs to create 100mL of a 38% acid solution. The chemist has a 20% and a 50% acid solution. How much of each must be mixed?
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.6.3 Mixture Problems with an Unknown Starting Amount (Part 2) Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.6.
- Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Mixture
Problems – Unknown Starting Amount (Part 2)”
Link: YouTube: Tyler Wallace’s Math Lecture Series: “Mixture
Problems – Unknown Starting Amount (Part
2)” (YouTube)
Instructions: Watch the video linked above, which discusses another mixture application. This example is like the above example except using coffee instead of acid.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
1.6.4 Mixture Problems with Pure Solutions Note: This subunit is also covered by the reading and assessment assigned in Subunit 1.6.
Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Mixture Problems – Pure Solutions” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Mixture Problems – Pure Solutions” (YouTube)
Instructions: Watch the video linked above, which discusses another mixture application. This application is similar to the two previous examples except one of the mixtures is pure.
You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.
Watching this video and pausing to take notes should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.