# Ch 4: Solving Algebraic Expressions & Equations

### About This Chapter

## Solving Algebraic Expressions and Equations - Chapter Summary and Learning Objectives

Start this chapter out on the right foot by learning how to determine the appropriate setup for math problem solutions. Then explore the strategies for understanding, evaluating, and simplifying expressions. Finish up with an abundance of practice in defining, translating and solving equations in both numbers and words. When you've completed all the lessons in this comprehensive chapter, you should feel confident in the following math concepts and operations:

- Evaluation of math formulas
- Combining like terms
- Negative signs in simplification of expressions
- Common algebraic equations
- Solving equations in number and word problems

Video | Objective |
---|---|

What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions | Show methods for using operations, numbers and math processes for solutions. |

Understanding and Evaluating Math Formulas | Take a look at various math formulas and determine which ones to use in specific problems. |

Expressing Relationships as Algebraic Expressions | Review the concept of algebraic expressions. |

Evaluating Simple Algebraic Expressions | Find out how to evaluate expressions by replacing variables with given values. |

Combining Like Terms in Algebraic Expressions | Explore methods for simplifying expressions by removing grouping symbols or combining like terms. |

Practice Simplifying Algebraic Expressions | Put your simplification skills into practice through exercises. |

Negative Signs and Simplifying Algebraic Expressions | Learn how to deal with negative signs when simplifying expressions. |

Writing Equations with Inequalities: Open Sentences and True/False Statements | Examine what is represented by inequalities, open sentence and true/false statements in equations. |

Common Algebraic Equations: Linear, Quadratic, Polynomial, and More | Take a look at the general format of quadratic, linear, general polynomial, cubic, radical and rational equations. |

Defining, Translating, & Solving One-Step Equations | Find out about the parts of equations, the process of translating into expressions and strategies for solving one-step equations. |

Solving Equations Using the Addition Principle | Use the addition principle for solving equations. |

Solving Equations Using the Multiplication Principle | Solve equations with the help of the multiplication principle. |

Solving Equations Using Both Addition and Multiplication Principles | Employ both principles to efficiently solve equations. |

Collecting Like Terms On One Side of an Equation | Practice determining whether like terms need to be collected on one side and the steps for doing so. |

Solving Equations Containing Parentheses | Learn to remove parentheses, collect like terms and solve equations with infinite or no solutions. |

Translating Words to Algebraic Expressions | Follow instructor's suggestions for translating words into algebraic expressions by changing words into symbols and identifying phrasing associated with arithmetic symbols. |

How to Solve One-Step Algebra Equations in Words Problems | Practice strategies for solving one-step problems expressed in words. |

How to Solve Equations with Multiple Steps | Learn the sequence for solving multi-step equations. |

How to Solve Multi-Step Algebra Equations in Word Problems | Use previously learned strategies to solve multi-step problems expressed in words. |

### 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 2 and Trig Textbook course

- Identifying Real Numbers
- Complex Numbers
- Absolute Value Review
- Calculating Rational Expressions
- Working with Linear Equations
- Solving & Graphing Inequalities
- Graphing & Working with Trigonometric Functions
- Graph Symmetry
- Graphing with Functions
- Solving Linear Equations
- Calculating & Graphing Polynomials
- Calculating & Simplifying Exponential Expressions
- Square Roots & Radical Expressions
- Quadratic Equations & Formulas
- Factoring & Graphing Quadratic Equations
- Conic Sections: Ellipses, Circles, Hyperbolas & Parabolas
- Vectors, Matrices and Determinants
- Exponential Functions & Logarithmic Functions
- Arithmetic & Geometric Sequences & Series
- Calculating & Presenting Statistics
- Combinatorics & Probability
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Equations
- Trigonometric Identities
- Circles, Angles & Circular Arcs