The length of the box is (30-2x) because you are removing x from both ends of the box
The width of the box is (6-2x) because you are removing x from both ends of the box
the height is x because when you fold up the flaps you've created they will come x high
Volume of a rectangular prism is length x width x height
plug in values
Expand if needed:
Domain is the possible values for x. Since this is a real 3D shape, l,w,h cannot be negative. The smallest x could be and not result in a negative value is x=0: l=30, w=6, h=0 although this wouldn't create a box just a flat piece of cardboard.
The largest would be what would make either w=0 or l=0
Since x=3 is smaller, this is the largest the x value can be since any bigger width would be negative.
Domain would be:
[0,3] <--- if you count a zero volume box to be valid
(0,3) <--- if you only count a box where V>0