1 5/6 - (x - 7/12) + 2 1/12 = 0.9

The answer is x=3.6 or 3 3/5.

First we convert the decimal answer to a fraction; 0.9 is read as "nine tenths," so the corresponding fraction is 9/10:

1 5/6 - (x - 7/12) + 2 1/12 = 9/10

Now we find a common denominator. The first thing that 6, 12 and 10 will all divide into is 60:

1 50/60 - (x - 35/60) + 2 5/60 = 54/60

Distributing the negative, we have:

1 50/60 - x + 35/60 + 2 5/60 = 54/60

Combining like terms, we have:

-x + 4 30/60 = 54/60

Subtracting 4 30/60 from each side, we have:

-x + 4 30/60 - 4 30/60 = 54/60 - 4 30/60

-x = - 3 36/60

Divide both sides by - 1:

-x/-1 = (-3 36/60) / - 1

x = 3 36/60 = 3 3/5 = 3.6