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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 .
Maclaurin's inequality is the following chain of inequalities: with equality if and only if all the are equal. For n = 2 {\displaystyle n=2} , this gives the usual inequality of arithmetic and geometric means of two non-negative numbers.
Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount; Bhatia–Davis inequality, an upper bound on the variance of any bounded probability distribution; Bernstein inequalities (probability theory) Boole's inequality; Borell–TIS ...
The UKMT runs a series of mathematics challenges to encourage children's interest in mathematics and to develop their skills. The three main challenges are: Junior Mathematical Challenge (UK year 8/S2 and below) Intermediate Mathematical Challenge (UK year 11/S4 and below) Senior Mathematical Challenge (UK year 13/S6 and below) [2]
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]
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. Some examples of inequations are:
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