SOLUTION: Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not? Give examples.

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Question 148452: Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not? Give examples.
Answer by mangopeeler07(462) (Show Source):
You can put this solution on YOUR website!
Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not? Give examples.

First off, this does not happen with equations because if you flip the equals sign, it's still an equals sign.

The inequality sign changes because you are switching the signs of the values in the inequality. So you must flip the inequality sign as well. Once all values become negative, that means that negatives are flipped from one side to the other (or abolished, if both sides were negative). If the sign is not flipped, it makes the solution a whole different range of numbers, because it changes the inequality. I will give you an example.

In the case where both sides are negative from the jump:
1.

How about we just skip flipping the sign and see what happens?

So right? Why don't we plug it back into the first one.

That works. Let's try something more than 2.

That doesn't work.

However if we flipped the inequality to begin with:

Then right?

Plug it back in
(We already know that 2 works, so skip it.)

It works!

*Going from positve to negative works the same way as above.

*In a case that one side is negative and the other is positive, make sure the inequality sign is always facing whichever sign (negative or positive) that it was facing originally.

Example:

More than or equal to faces the positive side. So when you multiply it by -1:

It still faces the positive side.