Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is not equal to another.

Front

What does the symbol '>' mean in inequalities?

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 inequalities?

Back

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

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x is any number greater than or equal to 2.

Front

What does the symbol '≤' mean in inequalities?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 7 means x is any number less than or equal to 7.

Front

How do you solve the inequality: 2x + 3 < 11?

Back

Subtract 3 from both sides: 2x < 8. Then divide by 2: x < 4.

Front

What is the solution set for the inequality x < -4?

Back

The solution set includes all numbers less than -4, such as -5, -6, -7, etc.

Front

What is the solution set for the inequality 6 < x < 10?

Back

The solution set includes all numbers between 6 and 10, not including 6 and 10.

Front

How do you express the inequality x > 4 and x < 12 in sandwich notation?

Back

In sandwich notation, it is expressed as 4 < x < 12.

Front

What is the solution to the inequality 3x - 10 > 2?

Back

Add 10 to both sides: 3x > 12. Then divide by 3: x > 4.