Question 113349: Can someone please help me with this problem. I am really confused on what to do PLEASE HELP ME!!!!
Add -2 to both sides of the inequality 5 > 3. Then divide both sides of the inequality -20 > -30 by -2. Explain in your own words what happens in both examples and when the direction of the inequality symbol is reversed.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! When you add or subtract from both sides of an inequality, the sense of the inequality stays the same, no matter what value you add or subtract. This works just like adding or subtracting to both sides of an equation.
So, if you add -2 to both sides of 5 > 3, you get 5 + (-2) > 3 + (-2), which is to say: 3 > 1. Notice that even though you added a negative number, the sense (the direction the inequality symbol is pointing) doesn't change. 5 is bigger than 3, and 3 is bigger than 1.
On the other hand, when you multiply or divide, the rules change. If you are multiplying or dividing by a positive number, then the inequality sense stays the same, but if you multiply or divide by a negative number, the sense of the inequality is reversed.
Let's look at your example: -20 > -30. We know that is true because -20 is ten units to the right of -30 on the number line and we know that as you move to the right on the number line, the numbers get bigger. But, when we divide both sides by -2, things change.  and  , so when we show the unequal relationship between 10 and 15, we have to reverse the inequality sign to keep the statement true. 10 < 15.
I hope this helps,
John
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