A point (point of action) is pulled left and right by strings with a vector F, creating balance. Will, can the force on the right be considered an inertial force ? At right end of the right string, a body with mass m is placed. In other words, tension ma is acting on the right string. In this pictere, the whole is moving to the left with a uniform acceleration.
Note: A website says, "Do not bring force into the cause of the motion (into its varying. also)."