Đáp án đúng: B
Giải chi tiết:\(\begin{array}{l}2 + \left| {x - 1} \right| = \left| { - 5} \right|\\2 + \left| {x - 1} \right| = 5\\\,\,\,\,\,\,\,\left| {x - 1} \right| = 5 - 2\\\,\,\,\,\,\,\,\left| {x - 1} \right| = 3\\TH1:\,\,\,x - 1 = 3\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\, = 3 + 1\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\, = 4\\TH2:\,\,\,x - 1 = - 3\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\, = 1 + \left( { - 3} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\,\, = - 2\end{array}\)
Vậy \(x = 4\) hoặc \(x = - 2.\)
Chọn B.