A mathematical inequality is a statement that compares two values or expressions, indicating that one is greater than, less than, or not equal to the other. Common symbols used in inequalities include >, <, ≥, and ≤. For example, the inequality 3 < 5 shows that 3 is less than 5. Inequalities can involve variables, such as x + 2 > 5, which means that the value of x must be greater than 3. Inequalities are essential in various fields, including algebra, calculus, and optimization. They help in solving problems where limits or ranges are involved, such as determining feasible solutions in linear programming. Understanding inequalities is crucial for analyzing relationships between quantities and making informed decisions based on those comparisons.