Writing Equations with Inequalities: Open Sentences and True/False Statements

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Common Algebraic Equations: Linear, Quadratic, Polynomial, and More

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:05 An Inequality
  • 1:00 The Four Inequalities
  • 2:10 True or False Statements
  • 3:16 Open Sentences
  • 3:42 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed
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.

After watching this video lesson you will be able to write open sentences and true or false statements that use inequalities. You will also be able to solve and/or determine whether a particular inequality is true or false.

An Inequality

Picture two pie slices with one being bigger than another. We can use inequalities to tell us which is bigger. What exactly is an inequality? Think of it as comparing the sizes of two values. The word 'inequality' literally means not exactly equal. So when we are using inequalities, our two values may not be equal and it is our job to figure out which value is the larger one.

To help us do this, we have symbols we can use. And these symbols actually are very good at telling us which one is bigger. For example, to say that 2 is greater than 1, we use the greater than symbol ( > ) and write 2 > 1. You can remember this sign easily because it looks like a mouth that is opening towards the bigger number. Who wouldn't want to eat the bigger number? It's like getting the bigger slice of pie!

The Four Inequalities

But, did you know that we have three other inequality symbols at our disposal? If we flipped our sign to look like this ( < ), we now have what is called the less than symbol. That's right, you guessed it! The smaller number is written first and the larger number second so that the mouth is towards the larger number. So we can write, for example, 1 < 2, and we read it as 1 is less than 2.

The other two symbols involve both the greater than and less than symbols. The only difference is that it tells us that we can also have the two sides equal. So we have the greater than or equal to symbol ( >= ) and the less than or equal to symbol ( <= ).

Greater than or equal to:


Less than or equal to:


For example, we can write 6 <= 6, or we can write 5 <= 6. We can also write 6 >= 6 or 7 >= 6. I can write 6 <= 6 or 6 >= 6 because both symbols allow for the numbers to be equal.

True or False Statements

Here is where we get into true or false statements. Sometimes we are given a problem that asks whether a particular inequality is true or not. For example, we may be asked to determine whether the statement 80 > 90 is true or not. How do you work with these problems? Well, you use your knowledge of counting and which numbers are larger to compare the numbers, and then you look at the symbol to see if it is the correct one.

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

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

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

Transferring credit to the school of your choice

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.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account