Epäyhtäläisyydet

Epäyhtäläisyydet, in English inequalities, are mathematical statements that compare two expressions using symbols other than the equals sign. The most common symbols used are: less than (<), greater than (>), less than or equal to (≤), and greater than or equal to (≥). For example, 5 < 10 states that 5 is less than 10, while x ≥ 3 indicates that the variable x has a value of 3 or any value greater than 3.

Solving inequalities involves finding the set of values for variables that make the statement true. The process is similar to solving equations, but with a key difference regarding multiplication or division by negative numbers. When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality symbol must be reversed. For instance, if we have -2x < 6, dividing by -2 reverses the inequality sign, yielding x > -3.

Inequalities are fundamental in various branches of mathematics, including algebra, calculus, and optimization. They are used to describe ranges of values, define constraints in real-world problems, and prove mathematical theorems. For example, in economics, inequalities can represent budget constraints, while in physics, they might describe the possible range of a physical quantity. The graphical representation of an inequality on a number line typically involves an open circle for strict inequalities (<, >) to indicate that the endpoint is not included, and a closed circle for non-strict inequalities (≤, ≥) to show that the endpoint is included.

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