Intro W1
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Objectives
- The sections for this week are:
- 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
- 2.2 Solve Equations using the Division and Multiplication Properties of Equality
- 2.3 Solve Equations with Variables and Constants on Both Sides
- 2.4 Use a General Strategy to Solve Linear Equations
- 2.5 Solve Equations with Fractions or Decimals
- The sections for this week are:
Intro and Learning Objectives (click on all tabs to see all sections)
2.1
Learning Outcomes
In this section, you will:
- Verify a solution of an equation
- Solve equations using the Subtraction and Addition Properties of Equality
- Solve equations that require simplification
- Translate to an equation and solve
- Translate and solve applications
Intro
Solving an equation is like discovering the answer to a puzzle. The purpose in solving an equation is to find the value or values of the variable that make each side of the equation the same – so that we end up with a true statement. Any value of the variable that makes the equation true is called a solution to the equation. It is the answer to the puzzle!
2.2
Learning Outcomes
In this section, you will:
- Solve equations using the Division and Multiplication Properties of Equality
- Solve equations that require simplification
- Translate to an equation and solve
- Translate and solve applications
Intro
You may have noticed that all of the equations we have solved so far have been of the form x+a=b or x−a=b. We were able to isolate the variable by adding or subtracting the constant term on the side of the equation with the variable. Now we will see how to solve equations that have a variable multiplied by a constant and so will require division to isolate the variable.
2.3
Learning Outcomes
In this section, you will:
- Solve an equation with constants on both sides
- Solve an equation with variables on both sides
- Solve an equation with variables and constants on both sides
Intro
In all the equations we have solved so far, all the variable terms were on only one side of the equation with the constants on the other side. This does not happen all the time—so now we will learn to solve equations in which the variable terms, or constant terms, or both are on both sides of the equation.
Our strategy will involve choosing one side of the equation to be the “variable side”, and the other side of the equation to be the “constant side.” Then, we will use the Subtraction and Addition Properties of Equality to get all the variable terms together on one side of the equation and the constant terms together on the other side.
By doing this, we will transform the equation that began with variables and constants on both sides into the form ax=b. We already know how to solve equations of this form by using the Division or Multiplication Properties of Equality.
2.4
Learning Outcomes
In this section, you will:
- Solve equations using a general strategy
- Classify equations
Intro
Until now we have dealt with solving one specific form of a linear equation. It is time now to lay out one overall strategy that can be used to solve any linear equation. Some equations we solve will not require all these steps to solve, but many will.
Beginning by simplifying each side of the equation makes the remaining steps easier.
2.5
Learning Outcomes
In this section, you will:
- Solve equations with fraction coefficients
- Solve equations with decimal coefficients
Intro
Many students do not feel very confident when they see all those fractions. So, we are going to show an alternate method to solve equations with fractions. This alternate method eliminates the fractions.
We will apply the Multiplication Property of Equality and multiply both sides of an equation by the least common denominator of all the fractions in the equation. The result of this operation will be a new equation, equivalent to the first, but without fractions. This process is called “clearing” the equation of fractions.
Readings
- Text: Read the sections from Openstax book Links to an external site. (Links to an external site.)
- Videos: Watch all the videos from "Resources W1"
Assignments
- Take Notes Week 1 These are the notes for all sections we cover in Week 1. Due Friday night.
Directions: Each section is accompanied by a Handout. Each Handout contains a few definitions, a few "How To" explanations, examples, and "Try It" exercises. Using the structure of the handout you have to write your own notes. Your notes must contain:
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- Your name
- The name of the section
- Definitions and "How To" from the provided handout (this is optional, however, it will be a good idea to have the complete notes)
- Everywhere there is a "Read Ex nr..." you have to read the example from the ebook and write in your notes : "I read the Ex nr..." . The link for the section in the ebook is provided at the bottom of the page.
- You have to solve ALL "Try It" exercises.
After you complete your notes you have to submit them. (See Take Notes Methods). Your files have to be pdf, jpeg, or jpg.
- Video quizzes Week 1 Due Saturday night 11:59pm
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- To learn the material for this sections, take notes while watching each video and then demonstrate what you learned by doing the exercise below it.
- Homework Week 1 Due Sunday night 11:59pm.
- There are 5 Homework this week. This are online Homework but you do not have to leave Canvas. Just click on each link, answer the questions, and came back for the next section. There is no partial credit, each question is either 100% good or not. However you have unlimited attempts for each question. A 5% per day penalty applies for Late work if you'll do it until Tuesday night. After that the Homework will be open only for practice.
THE DUE DATES FOR ASSIGNMENTS ARE FRIDAY SATURDAY AND SUNDAY. HOWEVER YOU CAN SUBMIT THEM UNTIL TUESDAY NEXT WEEK.
A 5% per day penalty applies for Late work if you'll do it until Tuesday night. After that the Homework will be open only for practice.
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