When does the sign flip in an inequality

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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.

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.

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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 64, 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! Read on to learn when you need to flip the inequality sign to solve an inequality correctly every time. You can even test your skills with some practice problems. Skip to Content.

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?

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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. Track your scores, create tests, and take your learning to the next level! Possible Answers:. Copyright holder you represent if other than yourself. Follow Us. Note that you might want to test a value close to your inequality to make sure that it works. If you were to choose you would see that the given inequality becomes: , which works because. I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process. Flip the inequality sign when you multiply or divide both sides of an inequality by a negative number. You reverse the inequality sign only when you multiply or divide by a negative number. To take the reciprocal, you just reverse the position of the numerator and the denominator.

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Reverse the inequality sign if you multiply or divide by a negative number on both sides. At this point: You could have added to both sides to get: And then when you subtract 8 from both sides you also end up at the correct answer:. In words, you would say "20 is greater than 6," and that's a true statement—so your solution checks out. Ling Certified Tutor. This gives you , matching the right answer determined above. Then add to both sides to isolate the variable on the right:. How to Divide Negative Numbers. When do you flip the inequality sign? Follow Us. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. Trending Articles How to.