Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality signs 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 2x + 3 > 7?

Back

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

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.

Front

What is the solution set for the inequality x < 5?

Back

The solution set is all real numbers less than 5.

Front

How do you graph the inequality x ≥ -3 on a number line?

Back

Draw a solid dot on -3 and shade to the right to indicate all numbers greater than or equal to -3.

Front

What does the phrase 'at least' indicate in an inequality?

Back

The phrase 'at least' indicates the use of the '≥' sign.