  Local available quantum correlations (LAQC), as defined by Mundarain et al.,
are analyzed for non-symmetric 2-qubit X states, that is, X-states that are not
invariant under the exchange of subsystems and therefore have local Bloch
vectors whose norms are different. A simple analytic expression for their LAQC
quantifier is obtained. As an example, we analyze the local application of the
amplitude damping channel for Werner states and general X states. Although this
local quantum channel can create quantum discord in some cases, no such outcome
is possible for LAQC, which hints toward their monotonicity under LOCC
operations. This work, along with our previous result for so-called symmetric
and anti-symmetric X states, completes the pursuit of exact analytical
expressions for the LAQC quantifier for 2-qubit X states.
