Back To Course

Supplemental Math: Study Aid1 chapters | 19 lessons

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jennifer Beddoe*

The less-than sign is a sign of inequality. It is represented by the < symbol. This lesson will describe the properties of less-than inequalities, show some example problems and provide a quiz at the end.

Mathematics is a language that uses many symbols. Learning all the symbols can be tricky, but it's critical for understanding what is being communicated, just like learning words and the rules for grammar is key to speaking and understanding a foreign language, like Spanish.

When two things are the same in every way, they are said to be **equal**. When two values are not the same, there is an **inequality**. In math, problems most often center around equations of numbers that are either equal or unequal. If the equations or numbers are not equal, it stands to reason that one of them is bigger than the other.

The **less-than symbol** (< ) is used to signify that the number on the left is smaller, or less, than the number on the right. The **greater-than symbol** (>) is used to signify that the number on the left is larger, or greater, than the number on the right. The less-than and greater-than symbols are actually the same symbol, the direction of which is switched depending on whether the number on the left is larger or smaller.

You may remember learning to use these symbols with the aid of an alligator when you were younger. The alligator is hungry, and so he opens his mouth towards the bigger number.

The less-than symbol, as well as the greater-than symbol, can be used for more than just showing which number is larger than another. In fact, many inequalities require you to solve the problems on each side of the less-than symbol in order to determine the relative value of a variable. Here is an example of a math problem containing the less-than symbol:

3*x* + 2 < *x* - 4

Just like you would if there was an equal sign, you want to group like terms together. Subtracting an *x* from either side, we get:

2*x* + 2 < -4

Subtract a 2 from either side to get:

2*x* < -6

Finally, dividing by 2, we have:

*x* < -3

You can see that solving an inequality is very similar to solving an equation. One important difference is our solution is not a single value. In this example, our solution includes all values less than -3.

Inequalities are common in everyday life. Many real-world examples of problems involving inequalities have to do with money. Sometimes you need to determine if you have enough money to purchase a specific item, or you may need to determine how much of something you can buy with the money you have. Here is an example in which understanding the less-than principle comes in handy:

Max wants to buy some t-shirts online. The t-shirts are $10 each and shipping will be $15. He only has $100 available to spend. How many t-shirts can he buy and stay within his $100 limit?

To solve this inequality, you first need to write an equation. Let *x* equal the number of t-shirts and the inequality should look like this:

10*x* + 15 < 100

This inequality states that $10 times the number of shirts plus $15 for shipping has to be less than the $100 Max has available to spend.

If you solve the inequality, you'll come to the solution *x* < 8.5. This means that the number of t-shirts Max can buy will be less than 8.5; he can purchase 8 t-shirts under his budget (since he cannot buy a fraction of a t-shirt). This is a simple example, but more complicated less-than/greater-than problems are tackled every day by finance professionals, architects, builders and people just living their daily lives.

The **less-than symbol** (<) represents an **inequality** in which the number or problem on the left is smaller than that on the right; however, it can be reversed (>) to show that the item on the left is greater than that on the right. These inequalities have everyday applications in a wide variety of areas, especially when dealing with money.

View this video lesson, then assess your capacity to:

- Identify and explain the use of the inequality symbol for less than
- Distinguish between the less than and greater than symbols
- Solve an inequality that includes the less than symbol
- Recognize the real-life applications of inequalities
- Turn an inequality word problem into a math equation

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

Create your account

Already a member? Log In

BackDid you know… We have over 79 college courses that prepare you to earn credit by exam that is accepted by over 2,000 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.

Back To Course

Supplemental Math: Study Aid1 chapters | 19 lessons

- Less Than Symbol in Math: Problems & Applications 4:10
- Trapezoid: Definition, Properties & Formulas 3:58
- What is Surface Area? - Definition & Formulas 5:56
- Using Parentheses in Math: Rules & Examples 3:58
- Universal Set in Math: Definition, Example & Symbol 6:03
- Complement of a Set in Math: Definition & Examples 5:59
- Zero Exponent: Rule, Definition & Examples 4:32
- Quotient Of Powers: Property & Examples 4:58
- What is Simplest Form? - Definition & How to Write Fractions in Simplest Form 5:49
- What is Slope? - Definition & Formulas 7:10
- Skewed Distribution: Examples & Definition 5:09
- Change Of Base Formula: Logarithms & Proof 4:54
- Transformations in Math: Definition & Graph 6:27
- What is Translation in Math? - Definition, Examples, & Terms 4:23
- Fixed Interval: Examples & Definition 4:00
- Scatterplot and Correlation: Definition, Example & Analysis 7:48
- Dilation in Math: Definition & Meaning 5:30
- Simplifying Fractions: Examples & Explanation 4:44
- Go to Overview of Math Concepts

- 8th Grade Language Arts
- MBLEx Test: Practice & Study Guide
- ICAS Mathematics - Paper F: Test Prep & Practice
- ICAS Mathematics - Paper E: Test Prep & Practice
- 7th Grade Social Studies: World History II
- Sustainable Economic Growth & Australia
- Reading Strategies Overview
- Sentences: Types & Parts
- Spelling Basics
- Ordering, Rounding & Factoring
- TExES Math 7-12 Test Dates
- FTCE Chemistry: Passing Score
- FTCE General Knowledge Test: Passing Score
- NCLEX Test Dates
- How Many Questions Are on the TExES PPR?
- How Hard is the CSET Social Science?
- How Hard is the CSET Multiple Subjects Test?

- Stress Management for Teachers
- Histrionic Personality Disorder: Symptoms, Treatment & Case Studies
- Bioenergetics: Definition & Theory
- Romanticism in Literature: Definition & Characteristics
- Materials Management: Planning & Process
- Silly Sally Lesson Plan
- Advertising Lesson Plan for Kids
- Deadweight Welfare Loss & Marginal Diagrams
- Quiz & Worksheet - X-Intercepts
- Quiz & Worksheet - Developing Students' Coping Skills
- Quiz & Worksheet - Diction in The Scarlet Letter
- Quiz & Worksheet - Action Words
- Quiz & Worksheet - Convex Lens
- Anterior Pituitary Hormones List & Flashcards
- Cnidarians List & Flashcards

- Nutrition 101: Science of Nutrition
- GED Math: Tutoring Solution
- FTCE Middle Grades English: Test Practice and Study Guide
- TExMaT Master Reading Teacher: Practice & Study Guide
- The Civil War and Reconstruction: Help and Review
- GACE Math: Functions
- WEST Math: Summarizing Data
- Quiz & Worksheet - Expressed vs. Implied Contracts
- Quiz & Worksheet - World Economies in the 18th Century
- Quiz & Worksheet - The Robber Barons of the Second Industrial Revolution
- Quiz & Worksheet - Statute of Limitations & Unconscionability in Contract Enforcement
- Quiz & Worksheet - Politics in the Gilded Age

- Reading about Shopping: Spanish Practice Activity
- Animal Cruelty Laws & Cases
- How to Pass a CLEP Test
- Illinois Real Estate Licensing & Continuing Education
- Homeschooling in Massachusetts
- How to Learn Java
- Professional Resources for Studying Medicine
- Georgia Biology Standards
- NCBTMB Recertification Requirements
- PSAT Test Dates
- Engineering Internships for High School Students
- Free Online Finance Courses & Certificates

Browse by subject