Back To Course

Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

Are you a student or a teacher?

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

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.

The **addition principle** tells you that if you add or subtract the same thing to both sides of an equation, then your equation will remain the same. You can picture the addition principle by thinking of two equal piles of stuffed animals, one on the left and one on the right with an equals sign in between. What if you added some more stuffed animals to the left side? How would you keep the two piles equal to each other?

You would have to add the same amount of stuffed animals to the right side. I mentioned sides, but the principle applies no matter which side you start with. The same goes if you took away some stuffed animals from the right side. To keep the two piles equal, you would have to take away the same amount of stuff from the left side.

Why is this useful? Well, when you want to solve an equation for a particular variable, you want to isolate your variable, or get it by itself. See, sometimes, you will see your variable being added or subtracted by a number. To solve and get your variable by itself, you would need to change this number to 0 so that it is no longer adding or subtracting from our variable. In order to do this, you sometimes have to add or subtract a value from the side with the variable.

But if you only did it to one side of the equation, your answer would be wrong. So, the addition principle tells you that you have to add or subtract the same thing to the other side of the equation as well so that your equation remains the same and your answer is correct. For example, for the equation *x* + 1 = 3, if we subtracted the 1 from the left side only to get *x* by itself, I would get *x* = 3.

But is that a correct answer? If I plug in 3 for *x* in my equation, I would get 3 + 1 equaling 4. Does 4 equal 3? No! So, I can't add or subtract from just one side; I have to do it to both. Think of your piles.

Let's solve *x* + 1 = 3 correctly now. We see that the side with our variable also has a plus 1. How do we make this plus 1 disappear or otherwise become 0? What can I add or subtract to this plus 1 to make it 0? I need to subtract a 1. The addition principle tells me that if I subtract a 1 from one side, I also have to subtract it from the other side. Let me see what I get when I do this.

*x* + 1 - 1 = 3 - 1*x* = 2

Ah, I get an answer of 2. Is this correct? Let me plug it back into my equation to see. 2 + 1 = 3 becomes 3 = 3. Does 3 equal 3? I think so. I am done. I have applied the addition principle, and my answer is correct!

Let's try another one.

*x* - 4 = 9

I look and I see that my variable is on the left side. Hmm, but it's not by itself. It is being subtracted by a 4. How do I change this minus 4 to a 0? I would have to add 4. I start to add 4 to the left side. But wait, what does the addition principle tell me? It tells me that if I only add 4 to one side, then my equation won't be the same and my answer won't be correct. I also need to add 4 to the other side. Oh, I'm so glad I remembered!

*x* - 4 + 4 = 9 + 4*x* = 13

Is 13 the correct answer? Let's check by plugging it back in.

13 - 4 = 9 becomes 9 = 9. Yes, another correct answer!

See if you can work this problem with me.

*x* - 8 = 8

What do we do to solve this?

*x* - 8 + 8 = 8 + 8

That's right; we need to add 8 to both sides.

*x* = 16

I get 16. Is that the correct answer?

16 - 8 = 8

8 = 8

Yes, it is!

This was a nice little video lesson, wasn't it? What did we learn? We learned that the **addition principle** tells you that if you add or subtract the same thing to both sides of an equation, then your equation will remain the same. This helps us solve problems when we have our variable being added or subtracted by a number that we want to move to the other side of the equation or otherwise make 0 on the side of the variable.

We learned that if we see the variable being added by a number, then we subtract that number from both sides of the equation to solve it. Also, if we see the variable being subtracted by a number, then we add that number to both sides of the equation to solve it.

This lesson can provide you with the knowledge you'll need to:

- Interpret the addition principle
- Solve basic equations using the addition principle

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackDid you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
11 in chapter 8 of the course:

Back To Course

Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions 5:50
- Understanding and Evaluating Math Formulas 7:08
- Expressing Relationships as Algebraic Expressions 5:12
- Evaluating Simple Algebraic Expressions 7:27
- Combining Like Terms in Algebraic Expressions 7:04
- Practice Simplifying Algebraic Expressions 8:27
- Negative Signs and Simplifying Algebraic Expressions 9:38
- Writing Equations with Inequalities: Open Sentences and True/False Statements 4:22
- Common Algebraic Equations: Linear, Quadratic, Polynomial, and More 7:28
- Defining, Translating, & Solving One-Step Equations 6:15
- Solving Equations Using the Addition Principle 5:20
- Solving Equations Using Both Addition and Multiplication Principles 6:21
- Collecting Like Terms On One Side of an Equation 6:28
- Solving Equations Containing Parentheses 6:50
- Solving Equations with Infinite Solutions or No Solutions 4:45
- Translating Words to Algebraic Expressions 6:31
- How to Solve One-Step Algebra Equations in Word Problems 5:05
- How to Solve Equations with Multiple Steps 5:44
- How to Solve Multi-Step Algebra Equations in Word Problems 6:16
- Algebra Terms Flashcards
- Go to High School Algebra: Algebraic Expressions and Equations

- Computer Science 336: Network Forensics
- Computer Science 220: Fundamentals of Routing and Switching
- Global Competency Fundamentals & Applications
- Introduction to the Principles of Project Management
- Praxis Elementary Education: Reading & Language Arts - Applied CKT (7902): Study Guide & Practice
- Practical Applications for Business Ethics
- Practical Applications for Marketing
- Practical Applications for HR Management
- Practical Applications for Organizational Behavior
- Analyzing Texts Using Writing Structures
- MBLEx Prep Product Comparison
- AEPA Prep Product Comparison
- ASCP Prep Product Comparison
- NCE Prep Product Comparison
- TASC Test Score Information
- What is the TASC Test?
- Praxis Prep Product Comparison

- Diclofenac vs. Ibuprofen
- Developing & Managing a High-Quality Library Collection
- Library Space Planning
- Literacy Strategies for Teachers
- Arithmetic Operations in R Programming
- Practical Application: Understanding Employee Behavior
- Positive Global Outcomes of Global Competence
- Practical Application: Color Wheel Infographic
- Quiz & Worksheet - Developing a Learner-Centered Classroom
- Quiz & Worksheet - Technology for Teaching Reading
- Quiz & Worksheet - Pectoralis Major Anatomy
- Quiz & Worksheet - Oral & Written Communication Skills
- Quiz & Worksheet - How to Teach Reading to ELL Students
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies

- AP Psychology: Homeschool Curriculum
- MCAT Prep: Help and Review
- CLEP Introductory Business Law: Study Guide & Test Prep
- English Composition: Certificate Program
- ILTS Science - Earth and Space Science (108): Test Practice and Study Guide
- High School Algebra - Complex and Imaginary Numbers: Tutoring Solution
- High School Algebra - Quadratic Equations: Tutoring Solution
- Quiz & Worksheet - Industrial Organizational Psychology History & Characteristics
- Quiz & Worksheet - Writing a Bio Poem
- Quiz & Worksheet - Types of Herbaceous Plants
- Quiz & Worksheet - C3 Plants
- Quiz & Worksheet - Couples' Relationship Building

- Reverse Transcriptase: Definition, Function & Structure
- SAT Math Level 2: Structure, Patterns & Scoring
- Texas Teacher Certification Renewal
- Free LSAT Practice Test
- Indiana Biology Standards
- Industrial Revolution Lesson Plan
- Casey at the Bat Lesson Plan
- Tennessee Science Standards for 8th Grade
- 7th Grade Arizona Science Standards
- South Dakota State Standards for Math
- Wisconsin State Teaching Standards
- Place Value Lesson Plan

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject