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# What is an inequality?

An inequality is simply an equation where (as the name implies) you don't have an equal sign. Rather, inequalities deal with more nebulous greater than/less than comparisons.

Let me use a real life example to communicate this.

You buy 300 chickens that you're going to cook at your restaurant tonight for a party. Your across-the-street rival Joe looks at your purchase and responds "tut tut, still a lot less than what I have," and walks away with a smirk.

If we were document this mathematically using an inequality, we'd get something like this:

Chickens you have ##<## Chickens Joe has

Remember the crocodile mouth from elementary school? That is pretty much all of what inequalities are about.

Now we also have what are called **inequality functions**. And those, as you may have guessed, simply look much like this:

##y< x##

Of course, the croc's mouth could be pointing both ways, and we could also have a ##<=## sign, which simply means "less than or equal to."

The graphs of these functions look very much like linear equations, as you can see below:

This graph represents the equation ##y > x##

This graph represents the equation ##y >= x##

As I mentioned before, inequality equations look very much like linear ones. However, if you notice, there's a shading on the left hand side of both graphs, and a dashed line on the ##y > x## graph.

This is simply because when you have an inequality, there is a vast of solutions that can satisfy the equation, a range not limited to a line. In the case of ##y >= x##, it's not just the coordinates on the line ##y=x##, but everything to the left of that as well.

In addition, with the ##y>x## graph, it is only everything to the left the line ##y=x##. **It does not include the line itself**. Hence, the line is dashed to indicate that it is not included in the function.

Hope my overly-thorough explanation helps :)