mapping class groups - Comparing geometric intersection numbers.

Let $a$, $b$, and $c$ be simple closed curves in an orientable surface $S$ such that
$i(a,b) geq 2$, $i(a,c) geq 1$, and $i(b,c) = 0$.
Let $w$ be a nontrivial element of the free group $langle T_a,T_b rangle$ which is different from $T_a^p$, $p$ nonzero integer, and set $x = w(a)$.
If $i(a,x) > i(b,x)$ and $n$ is a nonzero integer, is there a way to compare $i(a,T_c^n(x))$ and
$i(b,T_c^n(x)) = i(b,x)$ ?