ANSWER:

It is not permissible to be in a mixed gym with music. 

In the UK, all gyms allow free-mixing between men and women (as far as I know), and the women often wear very revealing clothes. There is often music played too. Is it permissible to go to these gyms and lower your gaze and put on headphones, if your intention is purely to get stronger for the sake of Allaah? I could work out at home but to get very strong it would help to go to the gym I think.

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