# Why do you not change the inequality sign when you are adding or subtracting?

##### 1 Answer

Because to do so would be algebraically incorrect. See below.

#### Explanation:

Consider the simplest of inequalities:

Now consider adding or subtracting a real number,

The only way to restore the inequality is to add or subtract

Thus:

So when must we reverse the inequality?

Consider where we multiply (or divide) both sides of the inequality by

As an example I will use

Then, if

So, in order to maintain the inequality after multiplying or dividing through by a negative number we must reverse the inequality.

Hope this helps. It's not as complicated as it seems!