Why Learn About Linear Equations?
Joan wants to travel but does not have a lot of extra spending cash. She read on several travel blogs that a good way to travel is to get a credit card with air miles and use it for all the things you normally budget for. This way, a big chunk of your airfare can be paid for with air miles.
She applied for and got a credit card with air miles. Joan has planned to use her air miles card for the following things each month:
- gas = [latex]$30[/latex]
- car insurance = [latex]$40[/latex]
- mobile phone bill = [latex]$65[/latex]
- groceries = [latex]$150[/latex]
- entertainment – restaurants, movies, and live music = [latex]$50[/latex]
Each dollar she spends gives her [latex]1.25[/latex] air miles, and she expects to need about [latex]1200[/latex] air miles to buy the ticket she wants. Joan would like to plan for how long to save so she knows when to start looking for a good deal on airfare, but is not sure how to make sense of all the details of her budget and airfare needs.
In this module, you will learn how to take information like Joan’s and translate it into mathematical equations that can help answer questions like, “How long do I need to save to take a trip?” We will revisit Joan at the end of this module and help her figure out how long she will need to use her air miles card so she can go on her trip.
Module 1 Learning Objectives
1.1: Solving One-Step Linear Equations
- Solve algebraic equations using the Addition Property of Equality
- Solve algebraic equations using the Multiplication Property of Equality
1.2: Solving Two-Step Linear Equations
- Use properties of equality to isolate variables and solve algebraic equations
1.3: Simplifying and Solving Linear Equations
- Apply the Distributive Property to simplify and then solve algebraic equations
- Combine like terms to simplify and then solve algebraic equations
- Use both the Distributive Property and combining like terms to simplify and then solve algebraic equations
1.4: Solving Linear Equations with Variables on Both Sides of the Equation
- Solving linear equations with variables on both sides of the equation
- Use both the Distributive Property and combining like terms to simplify and then solve algebraic equations with variables on both sides of the equation
- Classifying solutions to linear equations
1.5: Solving Equations Containing Fractions
- Use the properties of equality to solve one-step equations containing fractions
- Clear fractions in an equation and then solve the equation
- Solve multi-step equations containing fractions
- Solve a basic rational equation
1.6: Solving Equations Containing Decimals
- Solve one-step equations containing decimals
- Solve multi-step equations containing decimals
1.7: Applications Using Linear Equations
- Direct Translation – Translate to an algebraic equation and solve
- Consecutive Integers – Use an algebraic equation to find consecutive integers, consecutive even integers, or consecutive odd integers when given the sum
- Perimeter – Use an algebraic equation to find the dimensions of a rectangle when given the perimeter
- Comparison Applications – Given information about how two unknowns are related, use an algebraic equation to solve for the unknowns
1.8: Applications Involving Percent
- Use an algebraic equation to solve a basic percent question
- Use an algebraic equation to solve application problems involving percent
1.9: Applications – Variation
- Solve a direct variation problem
- Solve an inverse variation problem
- Solve a joint variation problem
- Solve application problems involving direct, inverse, and joint variation
1.10: Formulas
- Evaluate a formula for given values
- Solve for a specified variable in a formula