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I had to work during the Golden Week holidays, while people were enjoying them.
Is my sentence (which is not a real story) correct?
Thanks
LiJ
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While other people were enjoying them.

(Well, I was really working most of Golden Week-- I only took one day off to visit Ibaragi.)
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The first time I read your sentence, I thought you meant "...while most people were enjoying themselves" (that is, having fun). Then I thought you probably meant "whlie most people were enjoying the holidays." There's nothing actually 'wrong" about your sentence, but it might sound better with one of these alternatives:

I had to work during Golden Week, while most people were enjoying the holidays.

I had to work during Golden Week, while most people were free to enjoy the holidays.

(There's nothing wrong with "the Golden Week holidays" -- I just took "holidays" out of the beginning of the sentence because I thought it was more useful at the end, and I didn't want to repeat it.)
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Comments  
Mr. M. was much quicker than I was -- and his suggestion is perfect!
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khoffit was more useful at the end
Thanks, Knoff. Got it!
Mister MicawberI was really working most of Golden Week
I bet your clients(students) really appreciate your work.
Thanks, Mister.