How do I install a washing machine when the drain is 7.5 feet high?
I would recommend not doing what you suggest, here's why:

A typical rough-in for a clothes washing machine is as show in the picture below and consists of the following:


vent
2" p-trap
vertical section of 2" pipe above the p-trap
(an actual outlet box as shown is not required, you can just use the plan end of the pipe)


Your discharge hose will fit inside the 2" pipe opening and will usually enter the pipe about 6" to 8". This connection is not water/air tight.

The size of the p-trap and the vertical section of pipe are to accommodate for the flow rate of the washing machine's discharge. The p-trap will create a restriction to the flow and the vertical pipe allows for some head water to buildup without putting any back pressure on the washing machine's internal pump.



A p-trap is a must as it will prevent sewer gas from entering your house. The vent is required to protect the water seal of the p-trap but can be replaced with an air admittance valve depending on local codes.

I would imagine that if your machine can pump that high it will be near its limit and without any room for a vertical section of pipe to discharge into you will have to make the connection sold which will put additional back pressure on to the machine's pump (even more due to the pipe size only being 1.5") which will shorten the life span of the pump.