Mopeds must travel on the **right side of the roadway** when there is no passable shoulder. This is because, in the absence of a shoulder or when it is not possible to travel on it, mopeds, like other vehicles such as bicycles and special vehicles, must use only the essential part of the lane, staying as close as possible to the right edge of the roadway.

- **Driving on the right** is a general rule for all vehicles, especially in situations of reduced visibility, such as curves or hill crests. This ensures that the part of the roadway corresponding to the opposite direction is kept clear, avoiding possible collisions.

- Mopeds, like other vehicles that would normally use the shoulder, must adapt to these conditions and continue driving on the right side of the roadway when the shoulder is not available.

Therefore, the correct option is for mopeds to travel on the **right side of the roadway** in these circumstances.