  Beyond the simplest case of bipartite qubits, the composite Hilbert space of
multipartite systems is largely unexplored. In order to explore such systems,
it is important to derive analytic expressions for parameters which
characterize the system's state space. Two such parameters are the degree of
genuine multipartite entanglement and the degree of mixedness of the system's
state. We explore these two parameters for an N-qubit system whose density
matrix has an X form. We derive the class of states that has the maximum amount
of genuine multipartite entanglement for a given amount of mixedness. We
compare our results with the existing results for the N=2 case. The critical
amount of mixedness above which no N-qubit X-state possesses genuine
multipartite entanglement is derived. It is found that as N increases, states
with higher mixedness can still be entangled.
