Inequalities when do you switch the sign

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. 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. In other words, simplify both sides of the inequality, isolate the variable, and then eliminate the variable's coefficient.

However, there is one major difference between equations and inequalities: When solving an inequality, if you ever multiply or divide both sides by a negative number, you must reverse the inequality sign. What do I mean by "reverse" the inequality sign?

Change less than signs to greater than signs, and vice versa. Less than or equal to signs become greater than or equal to signs, and vice versa. I call this the inequality mood swing. Remember, it only happens when you multiply or divide by a negative number, and that only occurs when you're trying to eliminate the coefficient.

So, just remember to check for a negative coefficient as you're eliminating it, and reverse the inequality sign as necessary. When you solved equations, you were advised to do the same things to both sides of the equal sign. Follow the same steps now, but do everything to both sides of the inequality sign instead.