ulighedsforhold

Ulighedsforhold is a Danish term used in mathematics to describe the relation between two expressions expressed by an inequality. It denotes that one side is greater than, less than, or not equal to the other, using signs such as greater than (>), less than (<), greater than or equal to (≥), and less than or equal to (≤). The notion covers both strict inequalities and non‑strict inequalities and defines a set of values that satisfy the relation.

Solving an ulighedsforhold involves determining all values of the unknown variable that make the inequality true. The solution is often an interval on the number line, possibly empty or all real numbers. Fundamental rules include that adding or subtracting the same number on both sides preserves the inequality, while multiplying or dividing by a positive number does so as well; multiplying or dividing by a negative number reverses the inequality sign. Techniques such as factoring, sign analysis, and considering domain restrictions are commonly used.

Examples help illustrate the idea. Solve x − 3 < 5: this implies x < 8, so the solution set is all real numbers less than eight. Another example: −2 ≤ x ≤ 4 means x lies between −2 and 4, including the endpoints.

Ulighedsforhold appear across fields such as algebra, calculus, and optimization, where they define feasible regions or constraints. They also appear in programming for conditional logic and in economics or operations research for inequality constraints. The concept emphasizes how the relative size of quantities is used to determine allowable values and feasible solutions.