Inequality

As stated previously, an inequality can be a statement about the general location of a member within an ordered set, or it can be interpreted as defining a solution set or relation. For example, consider the compound expression 5 < x < 6 (read "5 is less than x, and x is less than 6") where x is a real number. This expression is a statement about the general location of x within the set of real numbers. Associating each of the real numbers with a point on a line (called the real number line) provides a way of picturing this location relative to all the other real numbers.

In addition, this same expression defines a solution set, or subset of the set of real numbers, namely all values of x for which the expression is true. More generally, an expression in two variables, such as y > 5x + 6, defines a solution set (or relation) whose members are ordered pairs of real numbers. Associating each ordered pair of real numbers with points in a plane (called the Cartesian coordinate system) it is possible to picture the solution set as being that portion of the plane that makes the expression true.