When does the sign flip in an 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:.

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. 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. To do this, subtract 6 from both sides. Since you're dividing by a negative number, you need to flip the inequality sign. The same rule would apply if you're multiplying both sides by a fraction. Multiplying and dividing are inverses of the same process, kind of like adding and subtracting, so the same rules apply to both. You also need to think about flipping the inequality sign when you're dealing with absolute value problems.

Which of the following represents the full set of values of that satisfy the above inequality? Copyright holder you represent if other than yourself.

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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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Example Question 8 : Understanding Inequalities. Starting with , you can:. Now, also recognize that you could have avoided the divide-by-negative step altogether. You Might Also Like. Atia Certified Tutor. 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. Trending Articles How to. At this point:. This image may not be used by other entities without the express written consent of wikiHow, Inc. Here you might divide both sides of the original inequality by to get alone.

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Then first of all you want to isolate the absolute value expression on the left side of the inequality it makes life easier. Reverse the inequality sign if you take the reciprocal of both sides. Company name. Then add to both sides to isolate the variable on the right:. By continuing to use our site, you agree to our cookie policy. Since you're dividing by a negative number, you need to flip the inequality sign. Subtract 6 from both sides to get:. Which of the following represents the complete set of values of that satisfy the inequality above? Starting with , you can: 1 Add 2 to both sides to get: 2 Divide both sides by 2 to get:. Correct answer:. Now, also recognize that you could have avoided the divide-by-negative step altogether. Which of the following represents the complete solution set for values of that satisfy the inequality above?