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This is a question that I started thinking about when I got a comment about this answer I posted:

Solving $\frac{x}{5}+\frac{x}{10}+\frac{x}{4}+75=x$

The question is well framed, and is almost a "yes/no" question. The OP asked "is my solution correct, and if so, why is it strange", and his solution was actually correct (if a bit confusing). Therefore, I answered by basically explaining that "yes, the answer is correct, and this is one possible reason for the strangeness of the answer"

The result? My answer received a downvote and a comment "But the question seems to be easily answered in comments" which seems strange to me.

My logic is that answers are answers, and comments are comments. I see no reason why an answer deserves a downvote just because it's short.

That said, I might be wrong. I don't mind taking a downvote, it's every user's decision about how to vote. However, there is also a more etherial concept of "community" at play here, and I want to know what the community overall thinks about comment-length answers. Are they really inappropriate?

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    $\begingroup$ Related: How to answer proof-verification questions? $\endgroup$ – quid Jan 13 '16 at 14:14
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    $\begingroup$ In fact it is answers posted as comments that are inappropriate. $\endgroup$ – Rahul Jan 14 '16 at 3:49
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    $\begingroup$ You didn't make the answer short enough:) $\endgroup$ – Winther Jan 14 '16 at 11:54
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    $\begingroup$ Note that receiving a downvote and deserving a downvote are two separate things that don't necessarily have any relationship to each other. There are SE users who downvote and don't comment and we will likely never understand most of the downvotes we get. If you get mostly downvotes, well then that's a good time to do some soul searching and honest evaluation of your post. If you get mostly upvotes, you just have to chalk the downvotes up to human nature and/or different points of view. $\endgroup$ – Todd Wilcox Jan 20 '16 at 15:00
  • $\begingroup$ Answering in a comment is a sneaky and unacceptable way to avoid a down vote, seems like in the SE network, the less trafficked sites see this more often. Good question! $\endgroup$ – JimLohse Jan 27 '16 at 2:46
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I don't think comment-length answers are inappropriate as long as they answer the question satisfactorily.

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    $\begingroup$ +1 for meta-answer on meta. $\endgroup$ – tomasz Jan 18 '16 at 22:28
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    $\begingroup$ +1 - there are WAY too many people that give a total and complete answer in the comments just because it's short. Comments are for comments, answers are for answers. It's WHAT IT IS that determines where it should go, not how long it happens to be. $\endgroup$ – Jimbo Jonny Jan 23 '16 at 20:37
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I think short answers are fine so long as they answer the question.

I have noticed that often full or partial answers are given in comments to questions but noone decided to post them as an answer. I don't know if they are afraid of being judged by potential downvotes, are not sure of their answer or something else?

Either way if you have answer that might help take courage and post it!

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Answers don't inherently deserve downvotes because they are short, but one-liners are generally inadequate as answers.

The Math.SE Community has a goal of curating excellent content, which means Questions and Answers that have value beyond the immediate ask and reply. If a user posts a very simple "verify my solution" problem, surely more can be said than just Yes or No.

In the type of Question you cite as an example, it could be pointed out that plugging in the proposed solution is a good way to go about verifying correctness.

When the OP expresses uncertainty about what ought to be a plainly correct answer, then I try to discern the cause of this uncertainty. Often there will be a confusion about definitions or mistaken application of a proposition where hypotheses are not satisfied. Spotting the cognitive difficulty usually requires some confirmation from the OP, but the effort can pay off in terms of actual learning.

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