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shake off = get rid of something, make something bad go away
examples:
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I can’t shake this cold off. I have been ill for almost two weeks.
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If you want to shake this cough off, drink a lot of liquids, juice, water, anything.
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I can’t shake off this thought that he might have lied to me.
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Let’s go out together. I want to shake off this depression.
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You can’t shake this fever off. Just go to the doctor.
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He can’t just shake off his bad reputation like that. People don’t forget easily.
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I want to shake off the image of the naive girl that people can take advantage of.
cover up = hide the truth about something
examples:
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They tried to cover up the scandal.
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You can’t cover up your past.
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They lied to everyone and covered the whole thing up for years.
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He made an error at work and tried to cover it up.
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If I make a mistake please cover up for me and I ‘ll try to fix it later.
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He didn’t steal the painting himself but he is covering up for somebody. He knows who did it and he is not talking.
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I am always covering up for you. Why can’t you be here on time before the boss arrives?