Place the carrots, potatoes, and onion into the bottom of a slow cooker, pour in the water, and place the brisket on top of the vegetables. Pour the beer over the brisket. Sprinkle on the spices from the packet, cover, and set the cooker on High.
Cook the brisket for about 8 hours. An hour before serving, stir in the cabbage and cook for 1 more hour.
