Officers were called at about 9:45 p.m. Sunday to a shooting in southeast Houston.
According to police, the argument may have started because the man brought his current girlfriend with him.
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The man was shot in the side and rushed to a local hospital, police said. He is expected to survive.
The shooting took place at the woman's grandmother's home, which is where the parents regularly meet for child drop-off.
Police have not released a description of the woman or her vehicle.
Anyone with information is urged to contact police.