A linear inequality is a mathematical statement that relates linear expressions using inequality symbols, indicating that one expression is either less than or greater than the other. It is a fundamental concept in algebra, often used to describe constraints in optimization problems and to define feasible regions in linear programming.

Linear Inequality

linear inequality

mathematical statement

Linear expressions are algebraic expressions that represent straight lines when graphed, consisting of variables and constants combined using only addition, subtraction, and multiplication by a constant. They form the foundation for understanding linear equations and inequalities, and are crucial in solving real-world problems involving proportional relationships.

linear expressions

Inequality symbols are mathematical notations used to compare two values or expressions, indicating whether one is greater than, less than, or not equal to the other. They are fundamental in expressing relationships in algebra, calculus, and various applied fields, enabling the formulation and solving of equations and inequalities.

inequality symbols

Optimization problems involve finding the best solution from a set of feasible solutions, often under given constraints. They are fundamental in various fields such as operations research, economics, and computer science, where the goal is to maximize or minimize an objective function.

optimization problems

feasible regions

Linear programming is a mathematical method used for optimizing a linear objective function, subject to linear equality and inequality constraints. It is widely used in various fields to find the best possible outcome in a given mathematical model, such as maximizing profit or minimizing cost.

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