From what I've read, it's not as simple as just cutting carbs and reducing inflammation. It depends on many factors. The source of the carbs. Are they highly processed carbs or whole grain carbs? What your lifestyle is like. If you're not active and get little exercise, then cutting carbs can be very beneficial. If you're active, then cutting carbs could cause some negative things to happen. Inflammation could also just be the result of your work and diet may not ever be able to overcome that. It's complicated.
Here's a decent page with lots info on the subject, with lots of reference links if you're curious about the actual scientific studies:
https://www.precisionnutrition.com/low-carb-diets