For an irrational real number$\alpha$ and real number $\gamma$ we consider the inhomogeneous approximation constant$$M(\alpha ,\gamma ):=\underset{\left|n\right|\to \infty }{lim\; inf}\left|n\right|\left|\right|n\alpha -\gamma \left|\right|$$via the semi-regular negative continued fraction expansion of $\alpha$$$\alpha =\frac{1}{{}_{}}$$