Ran over a safety razor on my right rear tire a couple of days back, no air is leaking. Was wondering if I could patch it up or do I have to get a new tire.
#Tire Cut
drowsy vigil
last quest
Honestly, I see no real problem here (and I'm a tire snob).
The sliced wedge isn't cool, I'll admit. In fact if it was me I'd probably try to clean the cut and use something like rubber cement to re-adhere it. Not sure it would make a damn bit of difference or even adhere for that matter. I'm just one of those that would try what I could.
If the slicing cuts deeper than the wear marks (you know that those are?) inside the rib I might think twice.
At first glance, your good.
drowsy vigil
I'll admit I'm not very knowledgabe about cars. I asked my uncle and he said it should be fine and told me about the rubber cement to glue the tires, but when I went to autozone they just told me to replace the tire and that any mechanic would recommend that. I'd just rather not spend for the tire if I dont have to.
subtle socket
Could put some sorta of rubber seal if you want to have a sense of reassurance 
last quest
I get it... And this tire isn't the worse I've seen. Would I take it on a track? Hell no... But it will survive daily drives without issue. Watch the area for signs of premature wear, but other than that, I stand by my comment that assumes the cut is not deeper than the minimum wear marks inside the inner rib.
If it is deeper than that, then meh, you've lost a margin of safety to consider. Relegate it to the rear and make sure your spare is ready just in case.