Your trouble is solving:
for a. I get a = 0.710723.
for b. I get b = 9.48772.
So your trouble is calculus, not statistics. Now that you know that what you're trying to do is correct, I suggest you go back and re-check your calculations. Then:
where the direction of the inequalities is maintained (that is, they are NOT reversed) because Y > 0. Y > 0 because Pr(Y > 0) = 1 (since Y has a gamma distribution)