Nesting "IF" Statements in Google Sheets to categorize numbers

I am trying to categorize numbers based on various levels of qualifications standards. For instance, Qualification "A" requires a number between 44.09 and 35.60. Qualification "B" requires a number between 35.59 and 29.30. Finally, qualification "C" requires a number at or less than 29.29. If the number is above the highest "A" qualification of 44.09, then an "X" should be displayed.

B2 happens to be the cell this formula is categorizing.

I have tried nesting "IF" statements in the following manner, however the formula incorrectly classifies the number.

=IF(44.09>=B2>35.59,"A", IF(35.59>=B2>29.29,"B", IF(B2<=29.29,"C","X")))

When I input "20" into "B2", the formula will classify it as "A", even though it should be "C".

Perhaps I have the "<>=" statements incorrectly stated, but I have tried fixing them to no avail. How can I change the formula to correctly classify these numbers?