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If a < b, prove that a < (a+b)/2 < b

The book had a different proof than the one I came up with. I understand the book's proof, I just want to know if my proof is also ok.

I did the following:

a < (a+b)/2 < b

2a < a+b < 2b

a < b < 2b-a

a-b < 0 < b-a

Since it was given that a < b, a-b must be less than 0, and b-a must be greater than zero, so the inequality a < (a+b)/2 < b is true if a < b.

Is this ok?

Thanks,

-GeoMike-

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# Verification of simple inequality proof

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