# How are these two equal?(equation, inequality)

Pithikos
How are these two equal??(equation, inequality)

I study discrete mathematics and we are doing combinations at the moment. There is this example in the book(Discrete Mathematics and Combinatorics p. 30 Ex. 1.43) where it states that the number of integer solutions for:

x1+x2+x3+x4+x5+x6<10 where xi$$\geq$$0

is equal to the number of integer solutions of

x1+x2+x3+x4+x5+x6+x7=10 where xi$$\geq$$0 and x7>0

Can someone explain me this? The author supposes that I magically understand what goes through his mind.

Here is a screenshot of the problem: http://img251.imageshack.us/img251/823/garbageab.jpg [Broken]

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