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.
