もしないで means "without even doing": something that should have come first was skipped, and the speaker finds that hard to believe. A verb goes into the ます-stem; with a する-verb, も sits between the noun and しないで, in place of を.
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She started putting it together without even reading the instructions.
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He signed the contract without even checking it.
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She ran off without even looking back.
もしないで or ないで
〜～ only says that something was not done. もしないで adds "not even", and with it the criticism.
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I went out without eating breakfast.
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He went out without even eating breakfast.
Usage notes
These go beyond describing what someone did.
Telling someone off
Before a command or a request, もしないで scolds.
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Don't go out to play without even doing your homework.
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Don't come into the room without even knocking.
もせずに
means the same and sounds more formal; it is the form you meet in writing.
is the old negative of
.
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It's dangerous to give an answer without even looking into it.
Lingaku