Solving Inequalities

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, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is greater than 5.

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'. For example, x < 3 means x is less than 3.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x is greater than or equal to 2.

Front

What does the symbol '≤' mean in inequalities?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 4 means x is less than or equal to 4.

Front

How do you solve the inequality -3 + x ≤ -11?

Back

To solve -3 + x ≤ -11, add 3 to both sides: x ≤ -8.

Front

What is the solution to the inequality 2x - 3 ≥ 4x - 1?

Back

To solve 2x - 3 ≥ 4x - 1, rearrange to get x ≤ -1.

Front

When graphing the solution to x < 5, what type of circle is used?

Back

An open circle is used for x < 5.

Front

When graphing the solution to x ≥ 3, what type of circle is used?

Back

A closed circle is used for x ≥ 3.

Front

Why do we use open circles for certain inequalities?

Back

Open circles indicate that the endpoint is not included in the solution set.