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.

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. For example, given , if you add to both sides and subtract 10 from both sides, you'll end up with , and now you will divide by positive 2, and not have to worry about sign-flipping to arrive at.

First, multiply both sides by 2 to eliminate the denominator:. Example Question 9 : Understanding Inequalities.

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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. The main situation where you'll need to flip the inequality sign is when you multiply or divide both sides of an inequality by a negative number. To solve, you need to get all the x -es on the same side of the inequality. Now isolate the x on the left side by moving the constant, 6, to the other side of the inequality.

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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Now you have a choice for how you move the remaining terms to isolate and solve for the variable. Reviewed by:. Now you want to get alone, so you can divide both sides by. The same rule would apply if you're multiplying both sides by a fraction. Flip the inequality sign whenever you multiply or divide both sides by a negative number. Explanation : Inequalities can be solved just like equations, with the only caveat that if you multiply or divide by a negative number you have to reverse the sign of the inequality. Addition and subtraction never change the direction of the inequality sign. A very important consideration when working with inequalities is that whenever you multiply or divide by a negative number, you must flip the inequality sign. That gives you: Then add to both sides to isolate the variable on the right: Divide by and you have your answer: , which is the same as. You also often need to flip the inequality sign when solving inequalities with absolute values. To take the reciprocal, you just reverse the position of the numerator and the denominator. Example Question 2 : Understanding Inequalities.

Last Updated: November 1, Fact Checked.

Taking the reciprocal is also useful when you're solving for a variable in the denominator of a fraction. Multiplication and division do change the direction of the inequality, but only if the number you're multiplying or dividing by is a negative number. Explanation : 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. Privacy Policy. Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects. Here that means that if you take the logical first step of dividing both sides by , you need to flip the inequality sign from greater-than to less-than, to get:. Elise Hansen is a journalist and writer with a special interest in math and science. Follow Us. Trending Articles How to. Solve inequalities using the same basic principles you use to solve equations.