# Ch 8: ELM Test - Algebra: Linear Equations & Inequalities

### About This Chapter

## ELM Algebra: Linear Equations and Inequalities: Chapter Summary

Study for the ELM Math using the online video lessons in this chapter. You'll cover the following topics:

- What is a Linear Equation?
- How to Write a Linear Equation
- How to Solve Linear Equations
- What is a System of Equations?
- What is an Inequality?
- How to Solve Linear Inequalities

Watch the videos in this chapter to learn the basics of these concepts, then test what you've learned using our online quizzes!

### ELM Objectives

The ELM is a math proficiency exam required for all incoming students to schools in the California State University system. You can learn more about the topics on the ELM here.

The lessons in this chapter are part of the Algebra topic of the ELM, which constitutes approximately 35% of the entire test. This chapter most closely addresses the 'solve linear equations and inequalities' objectives. Other objectives covered in this online course include:

- Evaluate and interpret algebraic expressions
- Simplify algebraic expressions
- Perform arithmetic operations involving rational expressions
- Solve quadratic and rational equations (with both numerical and literal coefficients; real solutions only)
- Solve problems in context that are modeled by quadratic equations
- Solve equations involving absolute value
- Solve inequalities involving absolute value

Watching the videos and taking the quizzes can help you master these central ELM topics and provide you solid foundation for the exam.

### 1. What is a Linear Equation?

Most cars won't be able to run for more than 250,000 miles, so how much longer will your car live? Linear Equations are the most basic kind of algebraic function and can help you answer questions exactly like this. Learn about what they look like, how they come up in your life and why they are powerful tools.

### 2. How to Write a Linear Equation

Simply knowing how to take a linear equation and graph it is only half of the battle. You should also be able to come up with the equation if you're given the right information.

### 3. Problem solving using Linear Equations

From sale prices to trip distances, many real life problems can be solved using linear equations. In this lesson, we'll practice translating word problems into linear equations, then solving the problems.

### 4. Solving Linear Equations with Literal Coefficients

In this lesson, we'll literally learn about literal coefficients. We'll look at how to solve linear equations that contain literal coefficients and practice solving several problems.

### 5. Solving Linear Equations: Practice Problems

With practice, linear equations can be straightforward to solve. In this lesson, we'll define linear equations and learn how to solve them. We'll look at multiple practice problems and walk through solving each one.

### 6. What is a System of Equations?

So what happens if we want to compare more than one equation? Welcome to a 'system' of equations! Learn what one is, how to solve them and when they come up in real life.

### 7. How Do I Use a System of Equations?

There are a few classic algebra word problems, such as the one about two trains traveling at different speeds. In this lesson, you'll learn how to take a word problem and convert it into the system of equations that will allow you to find the answer using either substitution or elimination.

### 8. Solving a System of Equations with Two Unknowns

When you have two variables and two equations, is solving the problem four times as hard? No! Not when you use the substitution or elimination method to solve systems of equations. We'll practice both in this lesson.

### 9. Solving Problems Involving Systems of Equations

Did you ever encounter a problem where you seem to have lots of information, but still have a couple of critical numbers missing? In this lesson, we'll practice solving word problems that require us to set up systems of equations.

### 10. What is an Inequality?

Deciding how to spend your money can be a tricky thing. Should you save it, invest it, or enjoy it? Learn how inequalities can help you make your decision!

### 11. Solving Linear Inequalities: Practice Problems

Linear inequalities may look intimidating, but they're really not much different than linear equations. In this lesson, we'll practice solving a variety of linear inequalities.

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### Other Chapters

Other chapters within the ELM: CSU Math Study Guide course

- ELM Test - Numbers and Data: Basic Arithmetic Calculations
- ELM Test - Numbers and Data: Rational Numbers
- ELM Test - Numbers and Data: Decimals and Percents
- ELM Test - Numbers and Data: Irrational Numbers
- ELM Test - Numbers and Data: Data & Statistics
- ELM Test - Algebra: Basic Expressions
- ELM Test - Algebra: Exponents
- ELM Test - Algebra: Absolute Value Equations & Inequalities
- ELM Test - Algebra: Polynomials
- ELM Test - Algebra: Rational Expressions
- ELM Test - Geometry: Perimeter, Area & Volume
- ELM Test - Geometry: Properties of Objects
- ELM Test - Geometry: Graphing Basics
- ELM Test - Geometry: Graphing Functions
- About the ELM Test
- ELM Flashcards