How to confront boyfriend about acting like he's single with other women?

asgv5126
I have been dating my boyfriend for almost a year now. He has always been very attentive and caring and always asking for more time together. I might be moving to a different city for work soon and he told me he would like to come with me. I am not a US citizen and he has even offered to marry me if I cannot find a job...

Yesterday he left his Facebook open on my phone and I looked at his messages. I was not happy about what I found. This older woman had messaged him saying how handsome he was. He said "thanks, you're not too bad to look at yourself" She then asked him to hang out and he took a couple of days to reply and then he said sorry I`ve been busy. She then messaged again asking "why do you think I gave you my number for?" ... the phone number was not on any message so I figured she did it in person. He just replied with a smiley face. She continues to message but he does not answer.Why does he not tell her he is in a serious relationship?

There was also another message with a girl saying "Hey you`re so cute hit me up" and her phone number. He did not tell her he had a girlfriend either.How do I confront him?

How to confront boyfriend about acting like he's single with other women?
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