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2. Inequality (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Inequality_(mathematics)

   For instance, to solve the inequality 4x < 2x + 1 ≤ 3x + 2, it is not possible to isolate x in any one part of the inequality through addition or subtraction. Instead, the inequalities must be solved independently, yielding x < ⁠ 1 / 2 ⁠ and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < ⁠ 1 / 2 ⁠.

3. List of inequalities - Wikipedia

   en.wikipedia.org/wiki/List_of_inequalities

   1.1.1 Inequalities relating to means. 1.2 Combinatorics. 1.3 Differential equations. ... Download as PDF; Printable version; In other projects Wikidata item; Appearance.

4. Inequation - Wikipedia

   en.wikipedia.org/wiki/Inequation

   In mathematics, an inequation is a statement that an inequality holds between two values. [1] [2] It is usually written in the form of a pair of expressions denoting the values in question, with a relational sign between them indicating the specific inequality relation.

5. Linear inequality - Wikipedia

   en.wikipedia.org/wiki/Linear_inequality

   Two-dimensional linear inequalities are expressions in two variables of the form: + < +, where the inequalities may either be strict or not. The solution set of such an inequality can be graphically represented by a half-plane (all the points on one "side" of a fixed line) in the Euclidean plane. [2]

6. QM-AM-GM-HM inequalities - Wikipedia

   en.wikipedia.org/wiki/QM-AM-GM-HM_Inequalities

   There are three inequalities between means to prove. There are various methods to prove the inequalities, including mathematical induction, the Cauchy–Schwarz inequality, Lagrange multipliers, and Jensen's inequality. For several proofs that GM ≤ AM, see Inequality of arithmetic and geometric means.

7. Triangle inequality - Wikipedia

   en.wikipedia.org/wiki/Triangle_inequality

   The first of these quadratic inequalities requires r to range in the region beyond the value of the positive root of the quadratic equation r 2 + r − 1 = 0, i.e. r > φ − 1 where φ is the golden ratio. The second quadratic inequality requires r to range between 0 and the positive root of the quadratic equation r 2 − r − 1 = 0, i.e. 0 ...