Solving 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?

Back

The symbol '<' means 'less than'. For example, 3 < 5 means 3 is less than 5.

Front

What does the symbol '>' mean?

Back

The symbol '>' means 'greater than'. For example, 7 > 4 means 7 is greater than 4.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 10 means x can be any number less than or equal to 10.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. For example, y ≥ 3 means y can be any number greater than or equal to 3.

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 is the solution to the inequality 10 - 3x < 16?

Back

Subtract 10 from both sides: -3x < 6. Then divide by -3 (remember to flip the inequality): x > -2.

Front

How do you graph the inequality x < 2?

Back

Draw a number line, place an open circle at 2, and shade to the left.

Front

What is the solution to the inequality 6x - 4 ≥ 26?

Back

Add 4 to both sides: 6x ≥ 30. Then divide by 6: x ≥ 5.

Front

How do you solve the inequality 3x - 2 < 13?

Back

Add 2 to both sides: 3x < 15. Then divide by 3: x < 5.