# Ch 14: Algebraic Expressions and Equations

### About This Chapter

## Algebraic Expressions and Equations - Chapter Summary

In this chapter, you'll learn how to solve both simple and more complex algebraic equations using basic mathematical principles. These include linear, quadratic, radical and rational equations, among other types. Each lesson will show you how to solve a different type of problem and is specific to the questions found on the mathematical reasoning section of the GED exam. Individual lessons will include topics in:

- Expressing and writing mathematical problems and relationships
- Understanding and evaluating mathematical formulas
- Collecting and combining like terms in an algebraic expression
- Simplifying algebraic expressions and equations
- Writing equations with inequalities
- Common algebraic equations
- Solving algebraic equations using addition and subtraction principles
- Translating words into algebraic expressions

### GED Math Objectives

The GED exam is a nationally established, high school equivalency exam that has been designed in accordance with the Common Core State Standards for grades 9 through 12. The 4-part test is taken on a computer and includes a mathematical reasoning section that requires 90 minutes to complete. Content emphasis is on algebraic and quantitative problem solving, with approximately 55% of the questions devoted to the former. Our video tutorials will cover all of the principles and topics found on the actual exam. Learning outcomes include the ability to:

- Define and apply the correct formulas to mathematical problems
- Define and evaluate algebraic expressions by replacing every variable with a given value
- Simplify algebraic expressions by combining like terms or removing grouping symbols
- Discuss inequalities, open sentence and true and false statements
- Distinguish among the different types of algebraic equations
- Identify the parts of an equation, and translate a sentence into an algebraic expression
- Solve one-step and multi-step algebra word problems
- Understand how to determine when a numerical expression is undefined

The mathematical content area on the GED tests a student's understanding of basic mathematical concepts, including those associated with critical thinking, problem-solving procedures and mathematical models. During the first part of the exam, test-takers will be provided with an on-screen, scientific calculator.

### 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.

### 19. What is Delta? - Definition & Concept

Delta is a letter of the Greek alphabet with several different mathematical meanings. Learn about the functions of delta, what it looks like, and how you can use delta in your mathematical expressions in this lesson.

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### Other Chapters

Other chapters within the College Algebra: Help and Review course

- Basic Arithmetic
- Overview of Real Numbers
- Foundations and Linear Equations: Help and Review
- Overview of Linear Equations
- Matrices and Absolute Value: Help and Review
- Inequalities: Help and Review
- Using FOIL, Graphing Parabolas & Solving Quadratics to Factor: Help & Review
- Properties of Polynomial Functions
- Working with Quadratic Equations
- Complex Numbers: Help and Review
- Exponents and Exponential Expressions
- Overview of Exponents
- Exponents and Polynomials: Help and Review
- Rational Expressions: Help and Review
- Working with Rational Expressions
- Math Expressions and Formulas
- Functions: Help and Review
- Fractions
- Factoring
- Exponentials and Logarithms: Help and Review
- Probability Mechanics: Help and Review
- Calculations, Ratios & Proportions
- Percent Notation
- Data, Statistics & Probability
- Sequences and Series: Help and Review
- Basic Number Sense and Operations
- Overview of Roots & Radical Expressions
- Overview of Continuity in Mathematics
- Overview of Mathematical Limits