When does the sign flip in an inequality

Last Updated: November 1, Fact Checked. Grace Imson is a math teacher with over 40 years of teaching experience.

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. Flip the inequality sign when you multiply or divide both sides of an inequality by a negative number.

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.

Note that you might want to test a value close to your inequality to make sure that it works. Which of the following represents the full set of values of that satisfy the above inequality? 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.

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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.

When does the sign flip in an inequality

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Reverse the inequality sign if you take the reciprocal of both sides. Example Question 7 : Understanding Inequalities. 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. Arts and Entertainment Artwork Books Movies. More References 2. Explanation : At first glance, you might simply multiply both sides of the original inequality by and believe that. If you plug that in to the given inequality you'll see that it does work, returning the true statement. Example Question 9 : Understanding Inequalities. First, multiply both sides by 2 to eliminate the denominator:. To do this, subtract 6 from both sides. If , which of the following must be true? Now, you need to rewrite this expression as a compound inequality. Do not fill in this field. No account yet? This is an untrue statement because 5 is not less than 4.

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.

Roger Cormier Apr 17, Popular Categories. When we multiply or divide by a negative, we have to flip the inequality sign, as we are basically "flipping" the relationship over 0 on the number line. Copyright Notice. Then first of all you want to isolate the absolute value expression on the left side of the inequality it makes life easier. Report an Error. Nov 13, This notification is accurate. Now isolate the x on the left side by moving the constant, 6, to the other side of the inequality. Which of the following represents the complete set of values of that satisfy the inequality above?