Back To Course

General Studies Math: Help & Review8 chapters | 85 lessons

Are you a student or a teacher?

Try Study.com, risk-free

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.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Norair Sarkissian*

In this lesson, we will examine the additive inverse of a given number. We will also learn about the additive inverse of a variable and how it can be represented graphically. Finally, we will explore the most widely employed application of the additive inverse.

The **additive inverse** of a number is what you add to a number to create the sum of zero. So in other words, the additive inverse of *x* is another number, *y*, as long as the sum of *x* + *y* equals zero. The additive inverse of *x* is equal and opposite in sign to it (so, *y* = -*x* or vice versa). For example, the additive inverse of the positive number 5 is -5. That's because their sum, or 5 + (-5) = 0.

What about the additive inverse of a negative number? Using the same approach, if *x* is a negative number, then its additive inverse is equal and opposite in sign to it. This means that the additive inverse of a negative number is positive. For instance, if *x* equals -12, then its additive inverse is *y* = 12. We can verify that the sum of *x* + *y* equals zero, since when *x* = -12 and *y* = 12, we have -12 + 12 = 0.

It should be noted that the additive inverse of 0 is 0. Zero is the only real number, which is equal to its own additive inverse. It is also the only number for which the equation *x* = -*x* is true.

We can also think of the additive inverse visually. Let's consider the real number line, which is usually drawn horizontally, with 0 near the middle, the negative numbers to its left, and the positive numbers on the right. Two numbers of opposite sign fall on either side of 0 on the number line at equal distance.

Once we place the point corresponding to a number *x* on the number line, we know that the additive inverse, or -*x*, will fall on the opposite side of the number line with respect to 0. In fact, the point 0 is the midpoint between *x* and its additive inverse -*x*. For example, when *x* = 5, its additive inverse is -5.

It is clear to see that the point 0 is the midpoint of the segment between -5 and 5.

Perhaps the most widely used application of the additive inverse involves the solution of linear equations. Let's consider the equation *x* + 7 = 10. The solution of this equation will be the value of the variable *x* for which the equation is true.

To isolate *x* on the left hand side of the equation, we need to get rid of the 7 on the same side of the equation. We can achieve this result by adding the additive inverse of 7 to both sides of the equation. The additive inverse of 7 is -7, and thus, we add -7 to both sides. The intended result is to 'zero out' the undesirable 7 on the left hand side of the equation, as follows:

Original equation: *x* + 7 = 10

Add -7 to both sides: *x* + 7 + (-7) = 10 + (-7)

Simplify: *x* + 0 = 3

Therefore, the solution of the equation is *x* = 3.

The **additive inverse** of a number is what you add to a number to create the sum of zero. So in other words, the additive inverse of *x* is another number, *y*, as long as the sum of *x* + *y* equals zero. The additive inverse of *x* is equal and opposite in sign to it (so, *y* = -*x* or vice versa). For example, the additive inverse of the positive number 5 is -5. That's because their sum, or 5 + (-5) = 0.

- The additive inverse of a number plus that number equals 0
- Ex: -5 + 5 = 0 , so -5 is the additive inverse of 5
- Additive inverse is often used in solving linear equations

After you've finished this lesson, you should be able to:

- Identify the additive inverse of a number
- Recall what additive inverse is

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

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did 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
2 in chapter 3 of the course:

Back To Course

General Studies Math: Help & Review8 chapters | 85 lessons

- Independent & Dependent Variables in Math 7:02
- Additive Inverse Property: Definition & Examples 3:53
- Fundamental Counting Principle: Definition & Examples 5:02
- What Is a Number Bond?
- What is an Abacus? - Definition & History 6:07
- How to Use an Abacus
- What is Regrouping in Math? - Definition, Subtraction & Addition 4:56
- The Lattice Method of Addition
- Modular Arithmetic: Examples & Practice Problems 6:23
- Modular Arithmetic: Rules & Properties 8:07
- What is Military Time? - Definition & Format 4:53
- What is Place Value? - Definition & Examples 6:05
- Composing & Decomposing Numbers
- Operations with Integers: Add, Subtract, Multiply & Divide 6:53
- Go to Basic Math Foundations

- Computer Science 109: Introduction to Programming
- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Early Civilizations & The Ancient Near East
- Fundamental Overview of World War I
- The Virginia Dynasty & Jacksonian America
- 1920's America and the Great Depression
- Building the United States After the American Revolution
- CEOE Test Cost
- PHR Exam Registration Information
- Claiming a Tax Deduction for Your Study.com Teacher Edition
- What is the PHR Exam?
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP

- Subtraction in Java: Method, Code & Examples
- Hydrogen Chloride vs. Hydrochloric Acid
- Extraction of Aluminum, Copper, Zinc & Iron
- Iroquois Culture, Traditions & Facts
- Noun Clauses Lesson Plan
- Adverb of Manner Lesson Plan
- Timeline Project Ideas for High School
- Quiz & Worksheet - Multi-Dimensional Arrays in C
- Quiz & Worksheet - What is a Diastereoisomer?
- Quiz & Worksheet - Mauryan Empire Art & Culture
- Quiz & Worksheet - What is a Convergent Sequence?
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- History Essay Topics for Teachers
- Common Core English & Reading Worksheets & Printables

- California Sexual Harassment Training: Employees
- NES Elementary Education Subtest 1 (102): Practice & Study Guide
- Sarah, Plain and Tall Study Guide
- Instructional Strategies for Teaching History
- CSET Physical Education Subtest III (131): Practice & Study Guide
- MTTC History: Revolution & Independence in Europe
- CEOE Marketing: Economics Overview
- Quiz & Worksheet - Russian & Central Asian Demographics
- Quiz & Worksheet - Reasons for Conflict & Cooperation Between Cultures
- Quiz & Worksheet - Influence of Environment on Agrarian Civilizations
- Quiz & Worksheet - Migration & Settlement in Caribbean, Central & South America
- Quiz & Worksheet - The US Oath of Allegiance

- Parallel Circuits: Definition & Concepts
- Allostasis vs. Homeostasis: Differences & Relationship
- Preschool Book List
- LSAT Registration Information
- Free LSAT Prep
- Best LSAT Prep Course
- 7th Grade Writing Prompts
- Weekly Progress Report Templates
- Interesting Topics to Study
- Why You Should Study Abroad
- How to Study Abroad After Graduation
- What is a Good PSAT Score?

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

Browse by subject