Linear Inequalities in One Variable

Front

What is a linear inequality?

Back

A linear inequality is a mathematical expression that shows the relationship between two expressions using inequality symbols (such as <, >, ≤, or ≥) instead of an equal sign.

Front

What does the symbol '>' mean in a linear inequality?

Back

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

Front

What does the symbol '<' mean in a linear inequality?

Back

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

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

Solve the inequality: 2x + 3 < 11.

Back

x < 4.

Front

Solve the inequality: -3x > 9.

Back

x < -3.

Front

What is the solution set for the inequality x ≤ 2?

Back

The solution set includes all numbers less than or equal to 2.

Front

How do you graph the inequality x > -1 on a number line?

Back

Draw an open circle at -1 and shade to the right to indicate all numbers greater than -1.

Front

What does the solution x < 5 look like on a number line?

Back

Draw an open circle at 5 and shade to the left to indicate all numbers less than 5.

Front

What is the difference between '≤' and '<'?

Back

'≤' means 'less than or equal to', while '<' means 'less than'. The former includes the endpoint, while the latter does not.