How does the inductive effect, explain the reactivity of tertiary alcohols with halogen acids?
Secondary and tertiary alcohols react with strong acid (and bases) such $\ce{HX}$ following SN1 mechanism.

$$\ce{ROH &lt;=&gt; HX + ROH_2^+ + X^-} \tag{1}$$
$$\ce{ROH_2^+ &lt;=&gt; R^+ +H_2O} \tag{2} $$
$$\ce{R+ +X- \rightarrow  RX} \tag{3} $$

In these reactions, the rate determining step is the formation of the carbocation (2). So the successive attack of the nucleophilic chlorides is dependent on that.



Here is how the inductive effect comes into play. The inductive effect of $\ce{R}$ groups of the alcohols stabilize the carbocation (figure show the stability of carbocations from the more stable to the less) and then increase the chances of a nucleophilic attack!