Inequality (mathematics).

Inequality (mathematics). Inequality (mathematics), mathematical relationship that makes use of the way in which numbers are ordered. Figure 1 shows the symbols used to denote inequality. For example, the inequality 3 < 10 says that the number 3 is less than the number 10. The inequality x2>= 0 expresses the fact that the square of any real number is always greater than or equal to zero. Inequalities often arise in describing areas and volumes. For example, if P is any point on the diagonal of the square shown in figure 2, then the area of the two rectangles that are shaded blue is always less than or equal to (<=) the area of the two squares that are shaded red. The solutions of an inequality such as -2x + 6 > 0 are the values of x for which the expression -2x + 6 is greater than zero. The rules of algebra can be applied to solve this inequality, except that the direction of the inequality must be reversed when multiplying or dividing by negative numbers. So, to solve the inequality -2x + 6 > 0, first subtract 6 from both sides of the inequality to get -2x> -6. Next, divide both sides of -2x> -6 by -2, reversing the direction of the inequality since -2 is negative. This gives x< 3, meaning that any value for x that is less than 3 will be a solution of -2x + 6 > 0. For the graphing of inequalities, see Graph. Contributed By: William James Ralph Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.