Funny you should mention it...
I've been running 32-bit Linux for a while, and have some experience with 32-bit asm programming. Recently I upgraded my system to 64 bit - Linux Mint Cinnamon. Now I'm completely lost!
I believe what we have to do is to install 32-bit libraries. I think we want to do this using "apt-get". I'm less sure, but I think what we want is "sudo apt-get install ia32-libs". This seems to "almost" work. It ends up at - of all things - a Microsoft EULA! This is totally unacceptable, but to keep the game going I'll play along and click "yeah, yeah, I accept". The first time I tried this was from a console - no mouse, and hitting "enter" didn't do anything. So just now, I tried it again from a terminal. This time I had mouse, but clicking "ok" didn't do anything, nor did any key combination I tried. Apparently, I am being blocked from installing Linux libraries I want by a Microsoft EULA.
I'm pretty sure my ultimate solution is going to be to flush Linux "Mint" and try another distro - I was running Slackware before and was happy with it. I'm trying to give it a fair trial and see if I can get used to it, but... it's crashed three times on me and popped up a Microsoft EULA more than once. I think it's history. Maybe you'll have better luck with it.
In the meantime, we can write 32-bit code that depends on system calls instead of the C library:
nasm -f elf32 myprog.asm
ld -melf_i386 -o myprog myprog.o
Be thankful for small favors!
Best,
Frank