võrratusi

Võrratusi, often translated as inequalities, are mathematical statements that compare two values or expressions using relational operators. Unlike equations, which state that two expressions are equal, inequalities assert that one expression is greater than, less than, greater than or equal to, or less than or equal to another. The common symbols used are >, <, ≥, and ≤.

Solving inequalities involves finding the set of values for variables that make the statement true. The process is similar to solving equations, with a crucial difference: multiplying or dividing both sides of an inequality by a negative number reverses the direction of the inequality sign. For example, if x > 5, then -x < -5.

Inequalities are fundamental in various areas of mathematics and its applications. They are used to define intervals on the number line, represent constraints in optimization problems, and form the basis for more complex mathematical structures like convex sets. In calculus, inequalities are used in proofs related to limits and convergence. In linear programming, inequalities define the feasible region for a set of solutions. Understanding and manipulating inequalities is a key skill for students and professionals in STEM fields.