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My prefix is one that can be just plain rude,
To get my infix, I think you may need to brood.
My suffix can be seen in the actions of angry dudes

All in all, I am something that 'eats food'

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I think the answer might be

Dissolvent

My prefix is one that can be just plain rude,

Dis = speak disrespectfully to or criticize.

To get my infix, I think you may need to brood.

Solve, you may need to brood in order to solve a problem

My suffix can be seen in the actions of angry dudes

Vent = let out a strong and sometimes angry emotion.

All in all, I am something that 'eats food'

A bit loose but the concept of dissolving could be seen as metaphorical for 'eating food'.

Title

This really is what put me on this track, the connection between the words solvable and dissolvent.

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    $\begingroup$ You are completely correct, especially the part about eating food, I was trying to make it all rhyme and it was the best fit. $\endgroup$ – Nobody Jan 23 at 16:43

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