An inequality says one expression is greater than, less than, or not equal to another. Symbols include , ≤, ≥, and ≠. The statement 3x + 2 > 8 means the left side exceeds the right for some values of x. Solving it gives x > 2.

Inequalities behave like equations in many ways, but there is a catch: multiplying or dividing by a negative number reverses the inequality sign. That rule trips up students, but it follows from the number line's order.

Inequalities describe ranges rather than exact values. They appear in optimization, where constraints are often inequalities. Linear programming uses systems of inequalities to find best solutions. In everyday life, inequalities express limits: speed must be ≤ 65, budget must be > 0, temperature should be between certain bounds. The concept is simple but powerful.

• Compares expressions that are not equal
• Symbols: , ≤, ≥, ≠
• Multiplying by a negative reverses the sign
• Used in optimization and constraints