Nested/Multiple IF functions in excel, how can I?

I am trying to implement an excel spreadsheet to keep track of my working hours.

I am entitled to unpaid breaks at my work, however these vary depending on the length of shift as follows.

0 - 3.75 hours = 0 min break

4 - 5.75 hours = 15 min break

6 - 7.75 hours = 30 min break

8 - 8.75 hours = 45 min break

9 - 11.75 hours = 90 min break

I would like to calculate my working hours minus breaks in excel.

I think I need to use if statement similar to the following (taking E2 as my hours):

=if(E2<=3.75, E2, if(4<=E2<=5.75, E2-30, if(6<=E2...etc...

But it never seems to work, can someone help me get this working???

Thanks.