Is it possible to install Linux on a single primary partition? I already have three primary partitions occupied by Windows 7 which I cannot give up.
Yes it is. There is no requirement for separate partitions in a Linux install, it's just a very good idea. Having certain partitions separate protects you from losing everything if a single partition fails. It is also good to have your
$HOME on a separate partition as that facilitates reinstalling or changing distributions.
However, you are free to set up Linux on a single partition and should have absolutely no problems with it.
A better option, however, is to create a fourth partition as an Extended Partition. That allows you to create multiple logical partitions within it and so have a Linux system with separate partitions for certain folders.
Using a LiveCD Linux such as ubuntu you can open
gparted (Gnome Partition Editor) to organize your hard disk.
You can then resize your primary partitions and create a new extended partition on the remaining free space. Then create at least two logical partition inside the extended one :
1. An ext4 partition for the system root filesystem
2. A swap partition with the 2*RAM as size.
Then you can start installing your Linux.