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Inequalities

What is an inequality?

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An inequality is the comparison of two numbers. Inequalities show if one number is greater than, less than, or not equal to the other. You can also use inequalities to show relationships like these:

  • greater than or equal to
  • less than or equal to

You have worked with inequalities in previous math classes. You used inequality symbols to represent unequal relationships between numbers. These symbols are shown below. Click each symbol to read what it means and see an example of how it is used.

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This is the less than symbol. It points to the left. You can use it to indicate that one number is smaller than the other.

If the school sold 73 tickets to the dance this year but only 32 tickets last year, they could compare this information using the inequality 32 < 73.

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This is the greater than symbol. It points to the right. You can use it to indicate that one number is larger than the other.

Another way the school can compare their dance ticket sales is by using the inequality 73 > 32. This is also a true statement.

You can use less than (\( \lt \)) and greater than (\( \gt \)) to represent an unequal relationship between numbers. Other inequality symbols you may have used in the past include less than or equal to (\( \leq ) \), greater than or equal to \( ( \geq ) \), and not equal to (\( \neq ) \). All the inequality symbols and their meanings are shown in the table below. Click each symbol to reveal its meaning and an example.

Symbol

Meaning

Example

less than

\( 3 \lt 4 \)

3 is less than 4

less than or equal to

\( 3 \leq 3 \)

3 is less than or equal to 3

greater than

\( 4 \gt 3 \)

4 is greater than 3

greater than or equal to

\( 4 \geq 4 \)

4 is greater than or equal to 4

not equal to

\( 3 \neq 4 \)

3 is not equal to 4

In mathematics, inequality relationships are just as important as equivalent relationships. These symbols allow us to compare numbers in a variety of different ways and to use the language of mathematics to represent different kinds of real-world situations.

Practice your knowledge of inequalities with the activity below. Match the statement in words on the left with its equivalent mathematical statement on the right.

To match items, click or tap an item in the left column and then click or tap its match in the right column. If you change your mind, make a different choice. Once you have matched all items, click "Check Answers" to see how you did. Click "Reset" to try again.
Great job!
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