How can I prove that the linear time search algorithm takes O (n) time?

The recurrence relation for the algorithm is an eccentric form that has an additional term: $ T (n) = T[frac{n}{2}] + T[frac{7n}{10} + 6] + n $. How can I prove that this recurrence relation leads to a complexity in time O (n)? The two common methods are iterative substitution and the main method, but none of them can be applied in an obvious way.