Solving and Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '>' mean in an inequality?

Back

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

Front

What does the symbol '<' mean in an inequality?

Back

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

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 4 means x is greater than or equal to 4.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 2 means x is less than or equal to 2.

Front

How do you solve the inequality x + 9 > 21?

Back

Subtract 9 from both sides: x > 12.

Front

What is the solution to the inequality 2x - 4 < 10?

Back

Add 4 to both sides: 2x < 14. Then divide by 2: x < 7.

Front

How do you graph the inequality x < 3?

Back

Draw a number line, place an open circle at 3, and shade to the left.

Front

What does an open circle on a number line represent?

Back

An open circle represents that the number is not included in the solution (e.g., x < 3).

Front

What does a closed circle on a number line represent?

Back

A closed circle represents that the number is included in the solution (e.g., x ≤ 3).