6. A uniform rod \(A C\), of weight \(W\) and length \(3 l\), rests horizontally on two supports, one at \(A\) and one at \(B\), where \(A B = 2 l\). A particle of weight \(2 W\) is placed on the rod at a distance \(x\) from \(A\). The rod remains horizontal and in equilibrium.

1. Find the greatest possible value of \(x\). The magnitude of the reaction of the support at \(A\) is \(R\). Due to a weakness in the support at \(A\), the greatest possible value of \(R\) is \(2 W\),
2. find the least possible value of \(x\).