# Inequations

From its name, you should be able to guess that *inequations*
have something to do with equations. In fact, the name is exactly the same
except for an ‘in*’* at the front. Equations are where you have two
expressions or sides, with an equals sign between them. This means that the
two sides are equal. Well, the ‘in*’* means ‘not’ in this case, so inequations
have two sides or expressions that are not necessarily equal.

There are several types of new symbols that are used in inequations. Here are some of them with an explanation of what they mean:

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### The *larger than* symbol:
>

Example use:

_{}

Whatever is on the left hand side of this symbol is
*larger than* whatever’s on the right hand side. For example, the first inequation
is saying that “five is larger than three”.

### The *smaller than* symbol:
<

Example use:

_{}

Whatever is on the left hand side of this symbol is
*smaller than* whatever’s on the right hand side. For example, the first inequation
is saying that “three is smaller than five”.

### The *larger than* *or*
*equals* symbol: ≥

Example use:

_{}

Whatever is on the left hand side of this symbol is
*larger than or equal* to whatever’s on the right hand side. For example,
the first inequation is saying that “five is larger or equal to 3”. Because it
says “larger than OR equal” it means that the number on the right hand side can
be either – it doesn’t have to be smaller, it can be the same value as the left
hand side. This means that there are two possible cases – one where the number
is smaller, and one where the number is the same size. _{} is one case where the
number is smaller.

The second inequation shows the other possible case where the numbers are the same size. It says that “five is larger than or equal to five”.

### The *smaller than* *or*
*equals* symbol: ≤

Example use:

_{}

Whatever is on the left hand side of this symbol is
*smaller than or equal* to whatever’s on the right hand side. Once again
there are two possible cases. _{} is one case where the left hand side
is *smaller than* the right hand side. _{} is the other case where the left
hand side is *equal to* the right hand side.

### How to remember these symbols

If you look at these symbols you can think of one side being ‘big’ and one side being ‘small’. The ‘size’ can be measured by the vertical size of the symbol at each side. The ‘taller’ side is the bigger side, where the larger numbers are.

To remember the “…or equal to” symbols, you just have to look for the equals sign in the symbol. Notice that it is always on the bottom part of the symbol, not the top part: