When does the sign flip in an inequality

You're sailing through your homework then An inequality with lots of negatives and absolute values. When do you flip the inequality sign?

Last Updated: November 1, Fact Checked. Grace Imson is a math teacher with over 40 years of teaching experience. She has taught math at the elementary, middle, high school, and college levels. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 59, times. Usually, you solve an inequality the same way you'd solve an equation, with one important difference—sometimes, you have to flip the inequality sign so it turns in the other direction. If you're not sure exactly when you need to do this, you're not alone!

When does the sign flip in an inequality

Which of the following expresses the complete set of values for that satisfy the inequality above? Inequalities can be solved just like equations, with one important caveat: if you multiply or divide by a negative number, you have to flip the inequality sign. Here, as you will see, there is no need to do that, so you can solve this just like you would an equation. First, multiply both sides by 2 to eliminate the denominator:. Next, add 2 to both sides to isolate the term:. Then divide both sides by 3 to get alone:. Which of the following represents the complete set of values of that satisfy the inequality above? This problem showcases an important concept about working with inequalities. If you multiply or divide an inequality by a negative number, you must flip the inequality sign. Here you might divide both sides of the original inequality by to get alone. If you do so, however, you must flip the sign to get:. You may wish to choose a number consistent with your answer to make sure that it satisfies the original inequality. If you were to choose you would see that the given inequality becomes: , which works because.

That gives us our two inequalities or our "compound inequality".

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Which of the following expresses the complete set of values for that satisfy the inequality above? Inequalities can be solved just like equations, with one important caveat: if you multiply or divide by a negative number, you have to flip the inequality sign. Here, as you will see, there is no need to do that, so you can solve this just like you would an equation. First, multiply both sides by 2 to eliminate the denominator:. Next, add 2 to both sides to isolate the term:. Then divide both sides by 3 to get alone:. Which of the following represents the complete set of values of that satisfy the inequality above?

When does the sign flip in an inequality

You're sailing through your homework then An inequality with lots of negatives and absolute values. When do you flip the inequality sign? No fear! There are a couple of occasions when you flip the inequality, and we'll go through them below.

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So you can solve this by doing the same thing to both sides of the inequality. Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects. Reader Success Stories. First, multiply both sides by 2 to eliminate the denominator:. If you've found an issue with this question, please let us know. Did this article help you? How to Determine Linear Equations. Follow Us. Grace Imson is a math teacher with over 40 years of teaching experience. A number that is larger when positive becomes "more negative," and thus smaller when negative, and vice versa. No fear! About This Article. Here you can start by multiplying both sides by 2 in order to eliminate the denominator. Purdue University-Main Campus, Doctor of Download Article Master inequalities with this super simple breakdown.

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Multiplying and dividing are inverses of the same process, kind of like adding and subtracting, so the same rules apply to both. How to Determine Linear Equations. Do not fill in this field. This image may not be used by other entities without the express written consent of wikiHow, Inc. If you do so, you'll need to flip the direction of the sign to get the proper answer:. Which of the following represents the complete solution set for values of that satisfy the inequality above? Log in Social login does not work in incognito and private browsers. Taking the reciprocal is also useful when you're solving for a variable in the denominator of a fraction. Elise Hansen is a journalist and writer with a special interest in math and science. Flip the inequality sign whenever you multiply or divide both sides by a negative number. How to Solve for a Variable. Copyright holder you represent if other than yourself.