Why is the following sentence correct?
Im Allgemeinen bin ich mit meiner Arbeit sehr zufrieden.
and the following wrong?
In allgemein bin ich mit meiner Arbeit sehr zufrieden.
Why "Allgemeinen" and not "allgemein"?
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Notice the presence of the definite article dem (hidden in im). So, im Allgemeinen is not a direct translation of in general, because there is no article in in general. (If there was one, it would rather be in the general in English, but this is not proper English, of course.) Other constructions which are analogue are:
To me, as a German native speaker speaking English as a second language only, it looks more like in general is the exception here, as it is omitting the definite article being common in other analogue constructions.
The definite article forces uppercase then, because Allgemeinen is a substantivized noun. For some rules have a look at the relevant section in Duden.