How is dividing each side of > x greater than 0 by a negative value different from dividing each side by a positive value?

Step-by-step explanation:

When you divide both sides of an inequality by a positive number, the inequality sign remains the same. When you divide both sides of an inequality by a negative number, you must reverse the inequality sign.

For example:

8 > 2 is a true inequality.

Let's divide both sides by 2:

4 > 1 is also a true inequality. The inequality sign remained > since we divided by a positive number.

Now let's start again with

8 > 2, and divide both sides by -2.

-4 > -1 is false. When the inequality sign remains the same after dividing both sides by a negative number, the inequality is no longer true. To keep the inequality true, we must change the inequality sign when dividing both sides by a negative number.

8 > 2

Divide both sides by -1.

-4 < -1 is true.

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step-by-step explanation: