# Ch 17: MTEL Middle School Mathematics: Principles of Algebra

### About This Chapter

## MTEL Middle School Mathematics: Principles of Algebra - Chapter Summary

This chapter seeks to prepare you for the MTEL Middle School Mathematics exam by reviewing the principles of algebra that may appear on it. Upon completing these lessons, you should be familiar with the following:

- Distribution with more than one term
- The use of algebraic expressions and strategies for evaluating them
- Commutative, associative, and distributive properties
- Combining like terms and simplifying algebraic expressions
- Addition and multiplication principles
- Graphing inequalities with one or two variables
- Solving linear inequalities

You can view these lessons as brief animated videos led by expert instructors, but you may also read their full transcriptions to take note of key highlighted terminology. Review the content at your own pace. If you have difficulty understanding any aspect of these lessons, you may consult our expert mathematicians for assistance.

### 1. Distribution of More Than One Term in Algebra

Once we've mastered distributing a single term, it's time to raise the stakes. In this lesson, we'll learn how about distribution involving two, three and even more terms.

### 2. Expressing Relationships as Algebraic Expressions

What do you do when you don't know what a number is but you do know how it relates to something else? You use an algebraic expression. In this lesson, we'll learn how to express relationships as algebraic expressions.

### 3. Evaluating Simple Algebraic Expressions

In this lesson, we'll learn how to evaluate algebraic expressions, which involves substituting numbers for variables and following the order of operations. By the end of the lesson, you'll be an algebraic expression expert.

### 4. The Commutative and Associative Properties and Algebraic Expressions

The order of operations is important and useful, but a few mathematical properties highlight cases where order doesn't matter. In this lesson, we'll learn about the commutative and associative properties, which may save you time and effort.

### 5. The Distributive Property and Algebraic Expressions

The order of operations is great. But sometimes we need to bend the rules to simplify an equation. Fortunately, the distributive property gives us a scenario in which this is okay. Learn all about it in this lesson.

### 6. Combining Like Terms in Algebraic Expressions

When you have an algebraic expression that's much too long, it would be great if you could simplify it. That's when knowing how to combine like terms comes in. In this lesson, we'll learn the process of combining like terms and practice simplifying expressions.

### 7. Practice Simplifying Algebraic Expressions

In this lesson, we'll practice simplifying a variety of algebraic expressions. We'll use two key concepts, combining like terms and the distributive property, to help us simplify.

### 8. 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.

### 9. 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.

### 10. How to Graph 1- and 2-Variable Inequalities

So an inequality is just an equation with a less than or greater than symbol. But what is the difference between 1 and 2 variable inequalities? What does have a greater than or equal to symbol change? When do you use a number line instead of a coordinate plane? Get those answers here!

### 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 MTEL Mathematics (Middle School)(47): Practice & Study Guide course

- MTEL Middle School Mathematics: Number Structure
- MTEL Middle School Mathematics: Absolute Value
- MTEL Middle School Mathematics: Math Properties
- MTEL Middle School Mathematics: Concept of Equality
- MTEL Middle School Mathematics: Operations
- MTEL Middle School Mathematics: Introduction to Fractions
- MTEL Middle School Mathematics: Operations with Fractions
- MTEL Middle School Mathematics: Decimals
- MTEL Middle School Mathematics: Percent
- MTEL Middle School Mathematics: Ratios, Proportions & Rate of Change
- MTEL Middle School Mathematics: Estimating
- MTEL Middle School Mathematics: Real Numbers
- MTEL Middle School Mathematics: Exponents
- MTEL Middle School Mathematics: Number Properties
- MTEL Middle School Mathematics: Roots & Powers
- MTEL Middle School Mathematics: Algebra Basics
- MTEL Middle School Mathematics: Functions
- MTEL Middle School Mathematics: Linear Equations
- MTEL Middle School Mathematics: Polynomials
- MTEL Middle School Mathematics: Quadratic Equations
- MTEL Middle School Mathematics: Vectors in Linear Algebra
- MTEL Middle School Mathematics: Matrices in Linear Algebra
- MTEL Middle School Mathematics: Patterns
- MTEL Middle School Mathematics: Measurement
- MTEL Middle School Mathematics: History of Geometry
- MTEL Middle School Mathematics: Properties & Theorems of Geometry
- MTEL Middle School Mathematics: Principles of Geometry
- MTEL Middle School Mathematics: Pre-Calculus Geometry
- MTEL Middle School Mathematics: Area, Perimeter & Volume
- MTEL Middle School Mathematics: Trigonometric Functions
- MTEL Middle School Mathematics: Trigonometric Graphs
- MTEL Middle School Mathematics: Solving Trigonometric Equations
- MTEL Middle School Mathematics: Trigonometric Identities
- MTEL Middle School Mathematics: Trigonometric Applications
- MTEL Middle School Mathematics: Data
- MTEL Middle School Mathematics: Probability & Statistics
- MTEL Middle School Mathematics: Probability & Science
- MTEL Middle School Mathematics: Calculating Probability & Statistics
- MTEL Middle School Mathematics: Logic
- MTEL Mathematics (Middle School) Flashcards