# inequality

**inequality,**in mathematics, statement that a mathematical expression is less than or greater than some other expression; an inequality is not as specific as an equation, but it does contain information about the expressions involved. The symbols < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to) are used in place of the equals sign in expressions of inequalities. As in the case of equations, inequalities can be transformed in various ways. The direction of the inequality remains unchanged if some number is added to both sides or subtracted from both sides or if both sides are multiplied or divided by some positive number; e.g., subtracting 10 from both sides of the inequality

*x*< 8 gives

*x*− 10 < −2, and multiplying the inequality by 2 gives 2

*x*< 16. Multiplication or division by a negative number reverses the sign of the inequality; e.g., if −2

*x*< 8, then dividing both sides by −2 results in the inequality

*x*> −4.

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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