*Macmillan Science Library: Mathematics*. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.

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## Solving Inequalities

Every possible equation can be made into an inequality. Furthermore, inequalities are solved the same way as equations, with one exception; namely, when an inequality is multiplied or divided by a negative number on both sides of the inequality sign.

For example, start with the true statement 5 < 6. When both sides are multiplied by -2, the statement becomes –10< –12. This resulting statement is false because –10 is greater than –12. Since multiplying (or dividing) an inequality by a negative number results in a false statement, the inequality symbol must be reversed to maintain a true statement. In this example, the correct answer is –10 > –12. As another example, to solve –4*x* > 12, divide both sides by –4, and then reverse the inequality to yield *x* < -3.

**A Practical Example.** Consider the following problem. A student has saved...

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