# Ch 2: Algebra II: Algebraic Expressions and Equations Review

### About This Chapter

## Algebra II: Algebraic Expressions and Equations Review - Chapter Summary and Learning Objectives

Use this chapter to get a refresher on some of the strategies used to solve word problems that ask you to find an unknown quantity. Instructors can show you how to cut a seemingly complicated problem down to size by translating key terms into basic arithmetic operations and solving for *x*. By the time you've finished viewing the lessons, you should be able to:

- Evaluate and solve simple algebraic expressions
- Simplify algebraic expressions containing both positive and negative signs
- Apply the addition and multiplication principles to solve an algebraic expression
- Develop an algebraic expression to solve a word problem

Video | Objectives |
---|---|

What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions | Learn how to set up mathematical expressions to solve word problems. |

Understanding and Evaluating Math Formulas | Get suggestions for reading mathematical formulas and choosing the right one to solve a problem. |

Expressing Relationships as Algebraic Expressions | Find out what a variable is and explore the use of algebraic expressions to add, subtract, multiply and divide. |

Evaluating Simple Algebraic Expressions | Learn how to substitute numbers for variables in an algebraic expression and solve it using the correct order of operations. |

Combining Like Terms in Algebraic Expressions | Explore the processes involved in combining like terms to simplify algebraic expressions. |

Practice Simplifying Algebraic Expressions | Understand how to combine like terms and use the distributive property to solve algebraic expressions. |

Negative Signs and Simplifying Algebraic Expressions | Explain how to simplify algebraic expressions by distributing negative signs. |

Writing Equations with Inequalities: Open Sentences and True/False Statements | Learn what an inequality is and find out how they're represented in true and false statements and open sentences. |

Common Algebraic Equations: Linear, Quadratic, Polynomial and More | Identify the differences between types of algebraic equations, including linear, quadratic, radical and rational. |

Defining, Translating, & Solving One-Step Equations | Learn how to turn key terms in a word problem into a 1-step mathematical equation. |

Solving Equations Using the Addition Principle | Demonstrate how the addition principle can be used to solve equations. |

Solving Equations Using the Multiplication Principle | Describe the use of the multiplication principle to solve equations. |

Solving Equations Using Both Addition and Multiplication Principles | Practice applying the addition and multiplication principles to the same equation in order to solve. |

Collecting Like Terms On One Side of an Equation | Identify and combine like terms in problems where they need to be collected on one side of an equation. |

Solving Equations Containing Parentheses | Show how the distributive property can be used to remove parentheses and combine like terms. |

Translating Words to Algebraic Expressions | Outline common terms associated with addition, subtraction, multiplication and division. |

How to Solve One-Step Algebra Equations in Word Problems | Apply your knowledge of terminology found in word problems to solve 1-step algebra equations. |

How to Solve Equations with Multiple Steps | Explain how to solve multiple-step equations by adding and subtracting first and then multiplying and dividing. |

How to Solve Multi-Step Algebra Equations in Word Problems | Identify steps for breaking down a word problem, writing an equation and solving it. |

### 1. What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions

When it comes to solving math word problems, there is a correct way of setting up the problem and labeling the various parts of the problem so that you can solve the problem easily. Watch this video lesson to learn how you can do it.

### 2. Understanding and Evaluating Math Formulas

With all the formulas out there, how do you know which one to pick? And how do you read formulas anyways? Watch this video lesson and you will find the answers to these questions.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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.

### 13. 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.

### 14. 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.

### 15. 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.

### 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. 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.

### 18. 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.

### 19. 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.

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### Other Chapters

Other chapters within the Algebra II Textbook course

- Algebra II: Basic Arithmetic Review
- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Matrices and Determinants
- Algebra II: Absolute Value Review
- Algebra II: Polynomials
- Algebra II: Factoring
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Quadratic Equations
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Conic Sections
- Algebra II: Sequences and Series
- Algebra II: Sets
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry