A real object is placed in front of a diverging lens, at a distance less than the focal length. When the object is moved slightly closer to the lens, which direction does the image move?

away from the lens.
doesn't move.
closer to the lens. -- I know this is the answer
But I am not sure about the question belowA real object is placed in front of a converging lens, at a distance greater than the focal length. When the object is moved slightly away from the lens, which direction does the image move?
away from the lens. -- would this be the correct answer?
doesn't move.
closer to the lens.

For a real object placed in front of a converging lens at a distance greater than the focal length, when the object is moved slightly away from the lens, the image will move closer to the lens.