They are both OK to my ear. The context already makes it clear that this is something one normally did, so the loss of "would" hardly changes the meaning.
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AnonymousJust to clarify, in both sentences, if i omit the word "usually", are both sentences still OK? Do they still imply things I would normally do in my last job when problem arised?Both versions still seem OK to me, and they both imply that you did those things every time there was a problem.
CliveIf I were the interviewer and you said 'usually', I'd ask 'Don't you always investigate a problem first and gather information? Why not?'You're a hard man!