When do you switch the inequality sign

Moreover, it is not difficult to see that a strictly decreasing function reverses both types of non-strict inequalities. The same explanation can be used for taking the reciprocal of both sides of an inequality, when both sides are positive or when both sides are negative.

Similarly, strictly increasing functions preserve inequalities. This gives a sometimes useful application of the calculus task of determining on what interval s a function might be increasing or decreasing, by the way. It looks like we're multiplying both sides by -1 and reversing the direction of the inequality. There's another way:. It's because negative numbers appear bigger but are actually smaller.

We need to flip the sign to make it true. For negative numbers, things are flip-flopped. NOTE : Multiplying by a negative is multiplying by a positive signs still same then multiplying by -1 Signs now flipped.

Dividing is multiplying by a fraction, and dividing by a negative number is multiplying by a negative fraction. Also, if you think about it, this also holds when you reciprocate both sides. Sign up to join this community.

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The Mongol Empire. The Most and Least Religious Countries. FEN Learning is part of Sandbox Networks, a digital learning company that operates education services and products for the 21st century. In solving multiple simultaneous inequalities using multiplication or division, the most important part is to solve each inequality separately and then combine them.

For many students, the above set of inequalities can best be understood graphically. The solution to the set of inequalities is the overlapping graphical area. 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.