Solving and Graphing Inequalities

Front

What is an inequality?

Back

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

Front

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

Back

The symbol '>' means 'greater than'. It indicates that the value on the left side is larger than the value on the right side.

Front

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

Back

The symbol '<' means 'less than'. It indicates that the value on the left side is smaller than the value on the right side.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side is either larger than or equal to the value on the right side.

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side is either smaller than or equal to the value on the right side.

Front

When do you flip the inequality symbol?

Back

You flip the inequality symbol when you multiply or divide both sides of the inequality by a negative number.

Front

How do you solve the inequality 2x + 3 < 7?

Back

Subtract 3 from both sides: 2x < 4. Then divide by 2: x < 2.

Front

How do you graph the inequality x > 3?

Back

Draw a number line, place an open circle on 3, and shade to the right to indicate all numbers greater than 3.

Front

What is the solution set of the inequality x ≤ 5?

Back

The solution set includes all numbers less than or equal to 5.

Front

How do you solve the inequality -3x ≥ 9?

Back

Divide both sides by -3 (remember to flip the inequality): x ≤ -3.