To solve this equation, we need to combine the different terms on the left side of the equation:

-9 5/6v + 2 3/4v + 1 5/12v = 1 7/27

First, convert all the mixed numbers to improper fractions:

-59/6v + 11/4v + 17/12v = 34/27

Then, find a common denominator for the fractions:

-354/36v + 99/36v + 68/36v = 34/27

Combine the fractions:

-187/36v = 34/27

Next, isolate the variable v by multiplying both sides by -36/187:

v = (34/27) * (-36/187)
v = -1224/5025

Therefore, the solution to the equation is v = -1224/5025.