võrratuste

Võrratuste, also known as inequalities, are mathematical expressions that compare two values or expressions, indicating that one is greater than, less than, or not equal to the other. They serve as fundamental tools in mathematics for defining ranges, constraining solutions, and modeling real-world relationships. Common inequalities include "greater than" (>), "less than" (<), "greater than or equal to" (≥), and "less than or equal to" (≤).

In algebra, inequalities are manipulated similarly to equations, with rules for addition, subtraction, multiplication, and division, bearing in mind the reversal of inequality signs when multiplying or dividing by negative numbers. Solutions to inequalities are often represented graphically on a number line, illustrating the set of all values that satisfy the inequality.

Inequalities are crucial in various fields such as economics, engineering, and science, where they are used to express constraints and optimize processes. For example, an inequality can specify the maximum capacity of a machine or the minimum amount of resources needed for a chemical reaction.

In systems of inequalities, multiple constraints are combined to define feasible regions within a coordinate plane. Methods like graphing, substitution, and linear programming are employed to analyze these systems and find solutions.

Overall, inequalities are essential for describing and analyzing conditions where certain limits or bounds are imposed, enabling decision-making and problem-solving in theoretical and practical contexts.