When do you flip the greater than sign

Explanations 3. Tommy San Miguel. Solving Inequalities: Multiplication by a Negative Number: Sometimes, it is necessary to multiply an inequality by a negative number in order to solve the inequality.

We'll try to move everything else to the other side. Here's why: Imagine comparing the numbers 5 and 3. Okay, now click over to the problems tab and give this technique a try! Related Lessons. Solve Inequalities with Addition or Subtraction — Examples. View All Related Lessons. Caroline K. Multiplying and Dividing by a Negative to Solve an Inequality When we multiply or divide by a negative to solve an inequality, it's the same as multiplying or dividing by a negative to solve a regular equation!

Multiplying by a Negative. Show Solution Check. Ben Ferrara. Get Link. You cannot divide by y or 5y since you do not know whether y is negative or positive and, as such, you do not know whether to flip the inequality. Solve each inequality alone. Combine each inequality and find the overlap i. 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.

Then first of all you want to isolate the absolute value expression on the left side of the inequality it makes life easier. Subtract 6 from both sides to get:. Now, you need to rewrite this expression as a compound inequality. The output of an absolute value expression is always positive, but the " x " inside the absolute value signs might be negative, so we need to consider the case when x is negative. That gives us our two inequalities or our "compound inequality". We can easily solve both of them.

These kinds of problems take some practice, so don't worry if you aren't getting it at first! Keep at it and it will eventually become second nature. You also often need to flip the inequality sign when solving inequalities with absolute values.

How to Divide Negative Fractions.