It sounds like your V-Brakes need to be centered. This is normal. Here's how you do it.
Before you get started, make sure that the wheel itself is nicely centered in the bike frame.
There is a tiny phillips screw on each brake arm. These are the centering screws. There are a number of ways to attack this issue, but the first way is to go to the brake that is too close to the rim. Turn this brake arm's centering screw inward, clockwise. Tightening this screw will have the effect of pulling that pad away form the rim. Here is a great, short video:
The whole video is only one and a half minutes long, but you can skip to Minute 0:49 to see the centering sequence. It's pretty straightforward. After you make an adjustment to one of the centering screws, give the handlebar brake lever a few squeezes to let everything settle and see what effect the adjustment had.
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