epäyhtälöjen

Epäyhtälöiden, or inequalities in English, are mathematical statements that compare two expressions using relational operators other than equality. These operators include "less than" (<), "greater than" (>), "less than or equal to" (≤), and "greater than or equal to" (≥). Unlike equations, which state that two expressions are equal, inequalities describe a range of possible values.

For example, the statement x < 5 indicates that the variable x can be any number smaller than 5. This includes numbers like 4, 0, -10, and so on. The statement y ≥ 2 means that y can be any number greater than or equal to 2, such as 2, 3, 100, or 2.5.

Solving inequalities involves similar techniques to solving equations, with one crucial difference. When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed. This is because multiplying by a negative number flips the relative positions of numbers on the number line.

Inequalities are fundamental in various areas of mathematics and science. They are used to define constraints in optimization problems, to describe the domain and range of functions, and in statistical analysis. The graphical representation of inequalities often involves shading a region on a coordinate plane, indicating all the points that satisfy the given condition. For instance, x + y < 1 would represent all points below the line x + y = 1.