Can I listen to iTunes purchases on Apple Music?

I'm not a music streamer and just want to listen to songs I've purchased on iTunes via my Android device. iTunes is not available on Android, but Apple Music is. I saw a claim that said that because of their integration, everything in your iTunes library can be combined with what you have on Apple Music. However, I downloaded Apple Music and it prompted me to pay $9.99 to use. How do I use a free version of Apple Music to listen to existing and future iTunes purchases?

If the answer is that it's not possible and there is no free version of Apple Music, my follow-up question is why would Apple offer to sync with your iTunes library? Seriously, what good would it do that you can listen to your old purchased songs when you're already paying monthly to access everything?