Can't add too much to the very good replies already posted, but I suspect that your instinct is correct - you should be able to safely commute. I don't know what your definition of "rough" is, however - only you can make that call.

I ride 7 miles each way from home to my job in Houston. While none of the neighborhoods I ride through are really bad (most are pretty fancy!), it's not uncommon to encounter a sketchy character or two. There aren't roving gangs or anything, however. I ignore them, avoid them, or run stop signs/lights if they're really freaking me out.

Normal commuting daylight hours are easy, lots of people out and about and drivers are generally polite (and know they have witnesses if they are jerks and bully me off the roads).

After dark things seem sketchier, yet I've biked by myself through downtown and the 6th ward at 10:30 pm a few times, and had no problems at all. I do run the lights at night though - feels safer to keep moving. Also, my normal commuting route sticks to side streets/bike lanes. If it's later at night, I switch to a main road and really take the lane to stay away from the sidewalks and potential weird people. It's 2 lane, so cars can pass easily, but it's much better lit and traveled, and I feel better knowing there are others around.

I get more creeped out on the dedicated bike paths along the bayou than I do on the street. WAY easier for someone to hide and attack in the parks.