# Ch 19: Saxon Algebra 1: Simplifying and Solving Equations

### About This Chapter

## How It Works:

- Identify the lessons in the Saxon Simplifying and Solving Equations chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the equations topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.

## Students will learn:

- One-step equations
- Conditional and equivalent equations
- Addition and multiplication principles
- The fractional-part-of-a-number equation
- Equations with mixed numbers and decimals
- Abstract and percent equations
- Equations with multiple steps and variables
- Negative coefficients and symbols of inclusion
- Distributive properties
- Translating math sentences to algebraic expressions
- Radical, rational and and varying equations

*Saxon is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. Defining, Translating, & Solving One-Step Equations

Watch this video lesson to learn how you can write a simple math equation when you are given a word problem. Learn how to translate words into math symbols. Learn the shortcuts to remember.

### 2. Simplifying & Solving Conditional Equations

Many equations are conditional equations. This lesson will define conditional equations and go over how to simplify and solve simple conditional equations using various rules.

### 3. Simplifying & Solving Equivalent Equations

When would two equations for one unknown variable be equal? Why would this information be useful? How would you solve for that variable and what would that variable mean? This lesson will explain all of these questions.

### 4. Solving Equations Using the Addition Principle

In algebra, we have certain principles that we use to help us solve equations quickly and easily. The addition principle is one of them. Watch this video lesson to learn how you can apply it to solve your equations.

### 5. Solving Equations Using the Multiplication Principle

When it comes to solving equations in algebra, one of the essential skills you need is the ability to multiply. Watch this video lesson to learn how you can use the multiplication principle to isolate your variable.

### 6. How to Use the Fractional-Part-of-a-Number Equation

This lesson will cover how to use the fractional part of a number equation. We will see how to set up this equation and how to use this equation to find the fractional part of a number. We will use real world examples to illustrate this process.

### 7. Abstract Equation: Definition & Concept

Being able to think abstractly is a great skill to have. Learn how abstract equations can help you in refining your abstract-thinking ability. Also, learn what some of them look like and memorize their applications.

### 8. Simplifying & Solving Equations With Decimals & Mixed Numbers

This lesson will review decimals and mixed numbers, and it will discuss how to convert between the two. We will then use examples to learn how to solve equations involving these types of numbers.

### 9. Percent Equation: Definition & Example

Percentages are everywhere, but have you ever heard of the percent equation? This lesson will explain the equation and give you several examples so you can use it to solve all of your percentage problems.

### 10. Solving Addition Equations with Two or More Variables

After watching this video lesson, you will know how to set up and solve addition problems where you have two or more variables. You will learn what steps you need to take to solve for each variable.

### 11. Solving Subtraction Equations with Two or More Variables

After watching this lesson, you'll be able to solve subtraction problems that involve more than one variable and more than one equation. Learn what steps you need to take and how to work with your equations.

### 12. How to Solve Equations with Multiple Steps

In algebra, when you want to solve an equation for a particular variable, you will need to perform multiple steps that include adding, subtracting, multiplying, and dividing. Watch this video lesson to learn the order you need to do these steps.

### 13. Solving Equations With Negative Coefficients

In this lesson, we will review what coefficients and negative numbers are. We will then talk about solving equations for a variable specifically when that variable has a negative coefficient.

### 14. Solving Equations That Have Symbols of Inclusion

Many mathematical equations involve symbols of inclusion. This lesson will define symbols of inclusion, show how to simplify expressions with these symbols, and explain the steps involved in solving equations with symbols of inclusion.

### 15. Solving Equations Using Distributive Property

In this lesson, we will go over the basics of the distributive property and how to use it. We will also talk about how to solve equations for a variable, particularly when those equations have parentheses in them.

### 16. Translating Words to Algebraic Expressions

When it comes to word problems, the easiest way to solve them is to look for keywords and change them into math symbols. Watch this video lesson to find out what keywords you should look for and what math symbols they represent.

### 17. Direct and Inverse Variation Problems: Definition & Examples

In this lesson, you'll learn how to approach questions about direct and inverse variation with a simple explanation of what the terms mean and how to apply them to problems.

### 18. Solving Equations Involving Variation

The concept of direct and indirect variation is quite common in our lives. In this lesson, we will look at the steps involved with solving equations involving direct and inverse variation. We will use an example that could easily be applicable to your life to illustrate the steps of the solving process.

### 19. How to Solve a Rational Equation

A rational equation is one that contains fractions. Yes, we will be finding a common denominator that has 'x's. But no worries! Together we will use a process that will help us solve rational equations every time!

### 20. Solving Radical Equations with Two Radical Terms

Solving equations with two radical terms takes some patience and care, but it really is not difficult. This lesson will show you the steps to solve these more complicated equations plus give you some examples to follow.

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### Other Chapters

Other chapters within the Saxon Algebra 1 Homeschool: Online Textbook Help course

- Saxon Algebra 1: Operations With Whole Numbers
- Saxon Algebra 1: Fractions
- Saxon Algebra 1: Decimal Numbers
- Saxon Algebra 1: Graphs on the Coordinate Plane
- Saxon Algebra 1: Sets
- Saxon Algebra 1: Real Numbers
- Saxon Algebra 1: Number Theory
- Saxon Algebra 1: Properties of Real Numbers
- Saxon Algebra 1: Conversion by Unit Multipliers
- Saxon Algebra 1: Ratio, Rate & Proportion
- Saxon Algebra 1: Percent
- Saxon Algebra 1: Exponents
- Saxon Algebra 1: Roots
- Saxon Algebra 1: Probability
- Saxon Algebra 1: Statistics
- Saxon Algebra 1: Simplifying Expressions
- Saxon Algebra 1: Polynomials
- Saxon Algebra 1: Simplifying Rational Expressions
- Saxon Algebra 1: Linear Equations
- Saxon Algebra 1: Quadratic Equations
- Saxon Algebra 1: Other Types of Equations
- Saxon Algebra 1: Understanding Functions
- Saxon Algebra 1: Lines, Points, Segments, and Planes
- Saxon Algebra 1: Angles
- Saxon Algebra 1: Polygons
- Saxon Algebra 1: Circles
- Saxon Algebra 1: Triangles
- Saxon Algebra 1: Geometric Solids
- Saxon Algebra 1: Perimeter and Circumference
- Saxon Algebra 1: Area
- Saxon Algebra 1: Surface Area and Volume
- Saxon Algebra 1: Pythagorean Theorem