That motherboard shows that it has a pci-express slot, I think the X1 stands for the number of the slots which is 1 on that motherboard. The pci-express x1 slots are totally different than pci-express x16.
The motherboard shown in the HP link provided by the OP should accept a modern video card... in other words it's NOT an X1 slot. However, the OP may be in for a world of disappointment if he's wanting to add a high-end video card to a system that will likely be limited by its PSU.
It is an HP A1250n system but I upgraded the ATI graphics card to the BFG 6600GT which made me have to upgrade the power supply.
I just check BFG's website and it says the 6600GT uses PCIe x16 so now I'm thinking I must be ok. I'm trying to get one off ebay so it will suck if it does not work.
Reviewing your pictures at wikipedia, mine definately looks like the larger one, so I am ok, right? (I think NightScope may have been right, the diagram of my motherboard that says 1X is just saying there is only one slot).
How do I find out what mine is 1x 4x 8x or 16x? Asus's website does not even recongize a A8Ae-LE motherboard.
I assume there are performance drawbacks putting a 16x card in a 1x,4x or 8x slot?