Inequalities - Research Article from Macmillan Science Library: Mathematics

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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 –4x > 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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This section contains 1,290 words
(approx. 5 pages at 300 words per page)
Buy the Inequalities Encyclopedia Article
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Macmillan Science Library: Mathematics
Inequalities from Macmillan Science Library: Mathematics. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.
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