LTM VE with VM server and Cisco Nexus deployment

Please forgive me but I am extremely new to the F5 world, so if what I am trying to portray doesn't make sense, I will do my best.

Here is what is going on at my site:

We have a new deployment of a 8 Dell R910 servers in 4 different clusters each for whatever, production, preprod, DMZ, etc. So these 8 servers will be connected to 2 Cisco Nexus 2232 --> to 2 Cisco Nexus 5596 --> existing Cisco 6509 VSS pair

We apparently have licenses for atleast 4 LTM VE, so the Web Operations section and the Network section are looking for the best practice on setting this up from an IP address perspective. The Web crew currently have a deployment with physical F5 LTMs where each server has a public facing IP and a private 192. IP address. That for every VM it needs a public (public to our company) and a private address with a 1 to 1 correlation. Like is server A is a 10.10.10.10 address then it's corresponding "F5 Network address" would be 192.168.10.10 and so on.

My quesion is can the F5s be put "in line) with the "public" network lets say again it's 10.10.10.0/24. Where if we were using 2 F5s to load balance a cluster of servers, each F5 would get an IP address on it and the a 3rd IP address would "float" between the two all in the same subnet. Also I'm not sure if it's relevant but all SSL would be offloaded at the F5

So my real end question is, does there need to be a seperate "F5 Network" for each "public" network we have, production (then an F5 Production network), pre-production (then a corresponding F5 pre-production network) or can the F5s each have one address is that same subnet and load balance the pool down to the servers?

I hope I am not being to confusing, I am trying to give as much information as I can without giving away any "company secrets"

I appreciate any help that can be provided

Thanks

Matt