Question

Question : Why do we reverse the direction of the inequality symbol when multiplying or dividing by a negative number ??

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Answer 1

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Explanation:

Hello!

Let's take an example: x > y

The rule that we currently have would state that -x < -y.

Now, let's substitute values for x and y. Say x is 5 and y is -3.

5 is greater than -3 (x > y), but -5 would be less than -3. (-x < -y). Hence the inequality would be true.

We can also take a look at this graphically on a number line. Turning a number negative is simply reflecting it over value 0.

As you can see, flipping the signs would change the values. To keep the inequality accurate, we reverse the inequality sign as well.