# Ch 12: ASVAB Math: Algebraic Expressions and Equations

### About This Chapter

## ASVAB Math: Algebraic Expressions and Equations - Chapter Summary

Dealing with algebraic expressions and equations may seem like a daunting task, but with the help of our easy-to-understand video tutorials, you'll be solving algebra problems left and right in no time. As you prepare for the ASVAB Math test, we'll walk you through the basic algebraic principles and practices, supply you with some helpful examples, and then let you test your knowledge with our fun self-assessments. These lessons cover:

- Simple and complex expressions and equations
- Equations with inequalities
- Linear, quadratic, and polynomial equations
- Addition and multiplication principles
- Equations with like terms
- Translating and solving equations that contain parentheses
- Multiple-step equations
- Real-world math problems
- Undefined numerical expressions

Our brilliant instructors have prepared these lessons in order to make understanding algebraic expressions and equations as easy as possible. Watch animated examples as you learn how to add, multiply, simplify, convert, and solve algebraic problems, and then try out our useful practice tests to see what you've learned.

## ASVAB Math: Algebraic Expressions and Equations Chapter Objectives

High school students and other candidates for the U.S. Military take the Armed Services Vocational Aptitude Battery (ASVAB) Math test throughout the year to determine their eligibility for enlistment. The paper-based Math Knowledge subtest is worth 11% of the exam and consists of 25 multiple-choice questions that you'll have to solve within 24 minutes. The computer-based Math Knowledge has 16 questions that must be answered within 20 minutes. The objectives for this chapter include:

- Conveying relationships as algebraic expressions
- Using open sentences and true/false statements
- Comprehending the differences between linear, quadratic, and polynomial equations
- Solving equations with the addition and multiplication principles
- Combining like terms and using parentheses
- Translating real-world problems into mathematical expressions
- Determining when numerical equations are undefined

The Math Knowledge subtest of the ASVAB includes questions that will require you to understand algebraic expressions and equations. Take some time getting to know our comprehensive video lessons so you won't have any problems facing algebra problems on the exam!

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. Negative Signs and Simplifying Algebraic Expressions

Don't let negative signs get you down. In this lesson, we'll stay positive as we practice simplifying algebraic expressions that have those tricky negative signs.

### 6. 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.

### 7. Writing Equations with Inequalities: Open Sentences and True/False Statements

After watching this video lesson you will be able to write open sentences and true or false statements that use inequalities. You will also be able to solve and/or determine whether a particular inequality is true or false.

### 8. Common Algebraic Equations: Linear, Quadratic, Polynomial, and More

Watch this video lesson to see the kinds of equations that you will come across most often in algebra. Learn to distinguish them by just looking for the identifying components of each equation.

### 9. 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.

### 10. 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.

### 11. Solving Equations Using Both Addition and Multiplication Principles

Most times in algebra, to solve for your variable, you will need to perform more than one operation to get your answer. Watch this video lesson to learn the proper steps to take to solve these equations.

### 12. Collecting Like Terms On One Side of an Equation

When you are using algebra to solve your problems, one of your biggest and most often used methods is that of collecting like terms. Watch this video lesson to see how it is done.

### 13. Solving Equations Containing Parentheses

When we have parentheses in our equations it changes the way we solve them. Now we have an added step to do to remove those parentheses. Watch this video lesson to learn how it is done.

### 14. 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.

### 15. How to Solve One-Step Algebra Equations in Word Problems

Word problems may be considered the most evil math invention ever, but never fear! Just watch this video lesson and you will know how to methodically translate these word problems into simple math and then to solve it.

### 16. 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.

### 17. How to Solve Multi-Step Algebra Equations in Word Problems

After watching this video lesson, you will be able to solve word problems like a pro. Learn how to setup your problem, write your equations and then solve your equations to find your answer.

### 18. How to Determine When a Numerical Expression is Undefined

We get all kinds of problems in math. We sometimes get numerical expressions that are undefined. Watch this video lesson to learn what it means to be undefined and how to find when a numerical expression is undefined.

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### Other Chapters

Other chapters within the ASVAB Mathematics Knowledge: Study Guide & Test Prep course

- ASVAB Math: Basic Arithmetic
- ASVAB Math: Math Expressions and Formulas
- ASVAB Math: Solving Math Word Problems
- ASVAB Math: Rounding Numbers and Decimals
- ASVAB Math: Fractions
- ASVAB Math: Factorials in Math
- ASVAB Math: Reciprocals
- ASVAB Math: Types of Numbers
- ASVAB Math: Patterns & Sequences
- ASVAB Math: Exponents
- ASVAB Math: Properties of Exponents
- ASVAB Math: Factoring
- ASVAB Math: Quadratic Equations
- ASVAB Math: Working with Quadratic Equations
- ASVAB Math: Inequalities
- ASVAB Math: Calculating Interest
- ASVAB Math: Circles
- ASVAB Math: Geometry
- About the ASVAB Test
- ASVAB Mathematics Knowledge Flashcards