What is an inequality in mathematics?

An inequality in mathematics is defined as a mathematical statement that describes the relative size or order of two values. This means that inequalities express how one value compares to another, indicating whether one value is greater than, less than, greater than or equal to, or less than or equal to another value. For example, in the inequality (x > 5), it is stated that (x) is greater than 5, providing direct information about the relationship between these two quantities.

In contrast to what it means to describe equality, which focuses solely on two values being equal, or an equation that merely represents a relationship between quantities through a specific equality, an inequality broadens the scope by encompassing a range of possibilities, highlighting the various ways values can relate to each other. Moreover, while some terms related to inequalities may involve variables, the concept itself isn't limited to equations or geometric formulas, which focus more specifically on shapes or precise calculations.

Thus, understanding that inequalities provide insight into relative size and order is fundamental to grasping many concepts in mathematics, from algebra to calculus and beyond.