New Install cannot run applications

Question

I've installed Arch in many systems usually with little to no problem, but this one takes the price.
I made a new installation on a brand new system.
I used the 64 bit version (but I do not think that really matters) and everything seemed well.
After I verified all the "basics" and added KDE4 I installed chromium from the repos. However, since I like Firefox for development I downloaded a copy from mozilla.org into my machine. This is NOT unusual.
I created a directory called Apps/firefix and put it in there. Again, this is standard procedure for me; it always works.
But this time ... something is NOT working so if I execute Apps/firefox/firefox I get: bash: Apps/firefox/firefox: No such file or directory
Of course that is not the case the files are  there.
I've been fooling around for hours now but I cannot see ANY reason for the problem.
My path is :
bash: /home/ralvez/bin:/home/ralvez/Apps:/home/ralvez/bin:/home/ralvez/Apps:/usr/local/bin:/usr/bin:/bin:/usr/local/sbin:/usr/sbin:/sbin:/usr/bin/core_perl: No such file or directory
I'm part of the following groups :
uid=1000(ralvez) gid=1000(ralvez) groups=1000(ralvez),5(tty),6(disk),91(video),92(audio),93(optical),94(floppy),95(storage),96(scanner),98(power),100(users)
Has anyone had a similar problem? Any ideas as to what could it be?
Thunks guys!!

Answer 1

@Trilby and Willian Richard,
I found the problem!! And I'll be dammed!! It is because I'm running a 64 bit OS.
If I go to mozilla.org and download a nightly binary made for 64 bit Linux OS then ... it works!
So ... the question now is:
How do we run a 32 bit application in a 64 bit OS? I know it is possible.
What people do in the Arch community? I'm sure I'm not alone in this quest... [looking worried ...] or am I
Ideas, solutions ?
Thanks!!