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-freeAlready registered? Log in here for access
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:
3x + 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:
2x + 2 < -4
Subtract a 2 from either side to get:
2x < -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:
10x + 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:
To unlock this lesson you must be a Study.com Member.
Create your account
Already a member? Log In
BackAlready registered? Log in here for access
Did you know… We have over 200 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.
Back To Course
Supplemental Math: Study Aid1 chapters | 19 lessons
{{courseNav.course.topics.length}} chapters | {{courseNav.course.mDynamicIntFields.lessonCount}} lessons | {{course.flashcardSetCount}} flashcard set{{course.flashcardSetCoun > 1 ? 's' : ''}}
Next Lesson
| 30 day money back guarantee | |||
|
Starting Original Price |
/yr | /mo | |
| Just Just | /day | ||
| Discount For months |
- % - | / | |
|
Price after trial Starting Price starting today |
/ | ||
| Just Just | /day | ||
| Save % off monthly plan | /mo | ||
| Just | /mo | ||
| Price | /yr | ||
Your Cart is Empty. Please Choose a Product.
Study.com video lessons have helped over 30 million students.
"I learned more in 10 minutes than 1 month of chemistry classes"
- Ashlee P.
"I aced the CLEP exam and earned 3 college credits!"
- Clair S.
Over 65 million users have prepared for {{displayNameByProductKey[registrationData.product || cocoon]}} and other exams on Study.com
"The videos have changed the way I teach! The videos on Study.com accomplish in 5 minutes what would take me an entire class."
- Chris F.
Over 65 million users have prepared for {{displayNameByProductKey[registrationData.product || cocoon]}} and other exams on Study.com
Over 65 million users have prepared for {{displayNameByProductKey[registrationData.product || cocoon]}} and other exams on Study.com
