For a diverging lens, the image is always real and inverted?

The main difference between a real image, and a virtual image and the statement you need to remember, is:

A real image can be displayed on a screen

A real image can be displayed on a screen or piece of paper or on a wall, whereas a virtual image can not.

A virtual image can be seen with the eyes but you can not display the image on a screen. It's not possible.

With a convex lens the light from an object passing through the lens can be projected on to a screen. 

With a concave lens only a virtual image can be seen. At no point can an image be projected or captured on a screen.

Notice, too, that with lenses:

Real images – always inverted
Virtual images – always upright

A real image is always inverted whereas a virtual image is always upright. 

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