Solving Inequalities: An Overview (page 1 of 3)

Sections: Linear inequalities, Quadratic inequalities, Other inequalities

Solving linear inequalities is very similar to solving linear equations, except for one small but important detail: you flip the inequality sign whenever you multiply or divide the inequality by a negative. The easiest way to show this is with some examples:

The rule for example 5 above often seems unreasonable to students the first time they see it. But think about inequalities with numbers in there, instead of variables. You know that the number four is larger than the number two: 4 > 2. Multiplying through this inequality by –1, we get –4 < –2, which the number line shows is true:

If we hadn't flipped the inequality, we would have ended up with "–4 > –2", which clearly isn't true.

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 Cite this article as: Stapel, Elizabeth. "Solving Inequalities: An Overview." Purplemath. Available from     http://www.purplemath.com/modules/ineqsolv.htm. Accessed [Date] [Month] 2016