adjective
1
BAD : I always feel anxious when I have to make a speech.
GOOD : I always feel nervous when I have to make a speech.
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anxious = worried because you fear that something bad may happen or may have happened: 'Their daughter hadn't come home from school and they were anxious about her safety.' 'I knew it was just a minor operation, but I couldn't help feeling anxious.'
nervous = worried because you are in or about to enter a stressful situation: 'I was so nervous about the exam that I couldn't sleep.' 'It was our first television appearance and we were all feeling nervous.'
2
BAD : She is anxious that the hotel rates will be too expensive.
GOOD : She is worried that the hotel rates will be too expensive.
BAD : I was anxious that somebody would see us through the window.
GOOD : I was worried that somebody would see us through the window.
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worried = unhappy because you have (or expect that you are going to have) a problem: 'The business is losing money and the boss is very worried.'
3
BAD : He obviously isn't anxious about public opinion.
GOOD : He obviously isn't worried about public opinion.
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not worried/concerned/bothered about sth = feeling that something is not a problem: 'I'm not bothered about how much it will cost.'
Note the alternative: 'He obviously doesn't care about public opinion.'
4
BAD : I'm anxious to hear about your new boyfriend.
GOOD : I can't wait to hear about your new boyfriend.
BAD : I am anxious to see how British people celebrate Christmas.
GOOD : I'm longing to see how British people celebrate Christmas.
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If you are anxious to do something, you want to do it in order to improve a (difficult or unpleasant) situation: 'We are anxious that people are informed of the truth of the matter.' 'The police are anxious to speak to anyone who witnessed the accident.'
If you simply have a strong desire to do something, you are keen/eager/longing/dying to do it, or you cannot wait to do it: 'I can't wait to get out of these wet clothes.'
5
BAD : Most unemployed people are anxious for finding work.
GOOD : Most unemployed people are anxious to find work.
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anxious to do sth (NOT for doing ): 'He was anxious to gain approval.'