Finding Volume triple integral by change of variables

[nautolian]

Homework Statement

∫∫∫_V 9z² dxdydz, where V is the solid defined by:

-1≤x+y+3z≤1, 1≤2y-z≤7, -1≤x+y≤1

Homework Equations

The Attempt at a Solution

I did this using the bounds, 1/3(-x-y-1)<=z<=(1/3)(-x-y+1), -x-1<=y<=1-x, -3/2<=x<=1/2 but I think the answer is wrong is there a better way to do this with change of variables? Thanks, any help would be greatly appreciated.

 

[LCKurtz]

Well, u = x+y+3z, v = 2y-z, w=x+y would surely give constant limits.