Here are some synonyms for "inextricably":
* Indissolubly
* Inseparably
* Intertwined
* Interconnected
* Closely linked
Here are some examples of how "inextricably" can be used in a sentence:
* The two friends' lives were inextricably linked. (Their lives are so closely connected that it's impossible to imagine one without the other.)
* The fate of the country was inextricably tied to the outcome of the war. (The war's result would have a permanent and unavoidable impact on the country's future.)
* History and culture are inextricably intertwined. (These two concepts are so deeply connected that it's impossible to study one without considering the other.)