Having these different approaches to determine a convenient value of k (number of clusters) should help to narrow down the options for $k$, however, we cannot make sure the value we select finally is the best or not. For example, if silhouette measure is closer to 1 when $k=5$ and for Inertia we have the "elbow" or "knee" around $k=4$ to $k= 6$, probably one of the values of 4, 5, or 6 might be a good value for the number of clusters. These two methods together help us have some estimations for the number of clusters but they do not guarantee it.
