Inequality

Examples

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.

Resources

Books

Bittinger, Marvin L., and Davic Ellenbogen. Intermediate Algebra: Concepts and Applications. 6th ed. Reading, MA: Addison-Wesley Publishing, 2001.

Davison, David M., Marsha Landau, Leah McCracken, and Linda Thompson. Prentice Hall Pre-Algebra. Needham, MA: Prentice Hall, 1992.

McKeague, Charles P. Intermediate Algebra. Fort Worth, TX: Saunders College Publishing, 1995.

KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Ordering relation

—An ordering relation is a rule for comparing the members of a set in a way that provides a method for placing each member in a specific order relative to the other members of the set. The integers, and the alphabet are examples of ordered sets.

Relation

—A relation between two sets X and Y is a subset of all possible ordered pairs (x,y) for which there exists a specific relationship between each x and y.

Set

—A set is a collection of things called members or elements of the set. In mathematics, the members of a set will often be numbers.

Solution set

—The solution set of an inequality is that subset of an ordered set which makes the inequality a true statement.