# How to write an absolute value inequality for each graph

Affiliate Even when the inequalities are more complicated, the above pattern still holds. And I really want you to internalize this visualization here. So this was the situation. I don't want to make a careless mistake there.

Now we don't care if it's above or below, we just care about the absolute distance fromor the absolute value of that difference, so we took the absolute value. To start, I look at the endpoints.

This is an example of case 3. Let's do it over here, too. In order for the absolute value of anything to be greater than or equal to 21, what does it mean?

But if we kind of keep our head on straight about what absolute value really means, I think you will find that it's not that bad.

### How to write an absolute value equation with given solutions

That's the equal sign. And all we care is that error, that absolute error, has to be a less than 2. Then solve the linear inequality that arises. The answer to this case is always all real numbers. So I want to adjust the inequality so it relates to —2. Now let's do one that's a little bit more complicated, that allows us to think a little bit harder. In particular, they're never negative. And I don't want you to just memorize it, but I'll give it to you just in case you want it.

Or you divide both sides of this by 7, you get x is greater than or equal to 3. Then click the button and select "Solve for x" to compare your answer to Mathway's.

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