An equation
The word says it all: equal.
In an equation, the left and right part are equal to each other. you might have the equation:
2
x
+
5
=
3
x
−
7
There is an
x
for which this is true. By solving this equation, you can find it. (see this as a challenge)
An inequality
The word says it all: inequal => NOT equal.
In an inequality, there are other symbols between the left and the right part. These symbols don't signify equality, but inequality. You have symbols like:
Greater than
>
Smaller than
<
Greater than or equal to
≥
Smaller than or equal to
≤
There usage is just as you might expect from their English meanings.
2
x
+
5
≤
3
x
−
7
Means that there is an
x
for which it is true, that
2
x
+
5
is less than or equal to
3
x
−
7
.
Hope this helped. Feel free to ask any follow up questions.