Matrices And Determinants

Let \(A = \left( {\matrix{ {[x + 1]} & {[x + 2]} & {[x + 3]} \cr {[x]} & {[x + 3]} & {[x + 3]} \cr {[x]} & {[x + 2]} & {[x + 4]} \cr } } \right)\), where [t] denotes the greatest integer less than or equal to t. If det(A) = 192, then the set of values of x is the interval :