Generator wiring

I am installing a portable generator to my breaker panel. There is already an unused 30 amp breaker that was attached to what was opnce a dryer connection. It is three wire and they have the white and black wire going to the breaker. To wire my generator outlet plug, it has a 4 connector 10/3. Rather than running a new 10/3 cable, can I just add another hot wire to the cable making it 4 wire and then use the black and red for hot and the white to the nuetral bar? Is this doable?

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Mark Cavinee
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