# Ch 8: Honors Algebra 1: Solving Algebraic Expressions & Equations

### About This Chapter

## Honors Algebra 1: Solving Algebraic Expressions & Equations - Chapter Summary and Learning Objectives

These lessons will help you learn how to identify and solve different complexities of algebraic expressions, equations and word problems. Our professional instructors will demonstrate the different procedures used to solve various equations and find solutions for word problems. After these lessons, you can take short multiple-choice quizzes to measure your skills:

- Solving equations using the addition and multiplication principle
- Collecting like terms on a single side of an equation
- Simplifying equations with infinite or no solutions
- Finding solutions for equations with multiple steps
- Using algebraic expressions to express and evaluate relationships
- Solving word problems with algebraic expressions and equations

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

Solving Equations Using the Addition Principle | Learn how to apply the addition principle to solve equations. |

Solving Equations Using the Multiplication Principle | Review how to use the multiplication principle to solve equations. |

Solving Equations Using Both the Addition and Multiplication Principle | Discover when to use both the addition principle and the multiplication principle. |

Collecting Like Terms On One Side of an Equation | Review how to collect like terms in an equation. |

Solving Equations Containing Parentheses | Find solutions for algebraic equations with parentheses. |

Solving Equations with Infinite Solutions or No Solutions | Distinguish between problems with no solutions or infinite solutions. |

How to Solve Equations with Multiple Steps | Use multiple steps to solve algebraic equations. |

Understanding and Evaluating Math Formulas | Review how to select and read formulas. |

Expressing Relationships as Algebraic Expressions | Use an algebraic expression to represent a relationship. |

Translating Words to Algebraic Expressions | Identify and convert key word in word problems to symbols. |

How to Solve One-Step Algebra Equations in Word Problems | Learn how to translate word problems into one-step equations. |

How to Solve Multi-Step Algebra Equations in Word Problems | Review how to translate word problems into multi-step equations. |

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. Solving Equations with Infinite Solutions or No Solutions

In algebra, there are two scenarios that give us interesting results. Watch this video lesson to learn how you can distinguish problems that have no answers and problems that have an infinite number of answers.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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 Honors Algebra 1 Textbook course

- Honors Algebra 1: Basic Arithmetic Review
- Honors Algebra 1: Fractions & Decimal Review
- Honors Algebra 1: Calculations, Ratios, Percent & Proportions
- Honors Algebra 1: Properties of Real Numbers
- Honors Algebra 1: Exponents & Scientific Notation
- High School Algebra: Radical Expressions
- Honors Algebra 1: Composing Algebraic Equations & Expressions
- Honors Algebra 1: Properties of Functions
- Honors Algebra 1: Absolute Value Expressions & Equations
- Honors Algebra 1: Matrices in Linear Equations
- High School Algebra: Working With Inequalities
- High School Algebra: Properties of Exponents
- High School Algebra: Properties of Polynomial Functions
- Honors Algebra 1: Vectors in Linear Algebra
- High School Algebra: Complex and Imaginary Numbers
- High School Algebra: Algebraic Distribution
- Honors Algebra 1: Linear Equations
- High School Algebra: Factoring
- Honors Algebra 1: Factoring with FOIL, Graphing Parabolas & Solving Quadratics
- Honors Algebra 1: Graphing & Factoring Quadratic Equations
- High School Algebra: Rational Expressions
- High School Algebra: Cubic Equations
- Honors Algebra 1: Descriptive Statistics
- Honors Algebra 1: Data Analysis
- Honors Algebra 1: Probability & Statistics
- Honors Algebra 1: Units of Measurement in Geometry
- Honors Algebra 1: Shapes of Geometry
- Honors Algebra 1: Similar Polygons
- Honors Algebra 1: Pre-Calculus Geometry
- High School Algebra: Well-Known Equations
- Honors Algebra 1: Maximum & Minimum Value of Functions
- Honors Algebra 1: Patterns in Math