Solving Inequality Systems: Finding Values of a and b

Translation: \begin{cases}x+a>b \ x-b<a \ \end{cases} Since solving inequality (1) gives x>b-a, and solving inequality (2) gives x<a+b, the solution set of the inequality system is b-a<x<a+b. Since the solution set of the inequality system \begin{cases}x+a>b \ x-b<a \ \end{cases} is -2<x<4, we have \begin{cases}b-a=-2 \ a+b=4 \ \end{cases}. Solving this system of equations gives a=3, b=1. Therefore, the answer is A.