An inequality is a mathematical statement that compares two expressions using symbols like <, >, β€, or β₯.
Inequalities express that one quantity is less than (<), greater than (>), less than or equal to (β€), or greater than or equal to (β₯) another. Solving inequalities involves similar steps to equations, but multiplying or dividing by a negative number reverses the inequality sign. Compound inequalities combine two conditions. Inequalities are used in optimization, interval notation, economics, and describing ranges of acceptable values.
Inequality symbols were introduced by Thomas Harriot in the 1631 book "Artis Analyticae Praxis" using > and <. The symbols β€ and β₯ were introduced by Pierre Bouguer in 1734 and later popularized by Leonhard Euler. The study of inequalities as a distinct branch of mathematics was developed in the 19th-20th centuries by mathematicians like Cauchy, Schwarz, and HΓΆlder.