Inequalities and Their Graphs

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other.

Front

What does the symbol '<' mean?

Back

The symbol '<' means 'less than'. For example, x < 5 means x is any number less than 5.

Front

What does the symbol '>' mean?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is any number greater than 3.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 4 means x can be any number less than or equal to 4.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x can be any number greater than or equal to 2.

Front

How do you represent the inequality x < 10 on a number line?

Back

You draw a number line, place an open circle at 10, and shade to the left to indicate all numbers less than 10.

Front

What is a solution to the inequality x > 5?

Back

Any number greater than 5, such as 6, 7, or 10, is a solution to the inequality x > 5.

Front

If x ≤ 9, what is a possible value for x?

Back

Possible values include 9, 8, 7, or any number less than 9.

Front

What does it mean if an inequality has an open circle on a number line?

Back

An open circle indicates that the number is not included in the solution set. For example, x < 5 means 5 is not included.

Front

What does it mean if an inequality has a closed circle on a number line?

Back

A closed circle indicates that the number is included in the solution set. For example, x ≤ 4 means 4 is included.