If $x succsim_i x_i^*$ then $p cdot x_ige w_i.$ (MWG 16.C.2)

(MWG 16.C.2) Suppose that the preference relation $succsim_i$ is locally nonsatiated and that $x_i^*$ is maximal for $succsim_i$ in set ${x_i in X_i: p cdot x_i le w_i}$. Prove that the following property holds: "If $x succsim_i x_i^*$ then $p cdot x_ige w_i.$"

Locally nonsatiation means that for every $x_i in X_i$ and $epsilon >0$, there exists $x_i’ in X_i$ such that $||x_i – x_i’|| < epsilon$ and $x_i’ succ x_i$.
I think that I need to prove that if $x_i sim_i x^*_i $ for $x_i not= x_i^*$, then it is possible that $pcdot x_i = w_i$ because I already know that if $x_i succ x_i^*$, then $pcdot x_i > w_i$.

I am stuck and cannot proceed. Can anyone give me some hint for this question?