Given that |x−1|+|x−2|+|x−3|≥6 Case 1: Whenx>3 (x−1)+(x−2)+(x−3)≥6 x≥4 Therefore, the value of x∊[4,∞) Case 2: When 2<x<3 (x−1)+(x−2)−(x−3)≥6 x≥6 Therefore, no possible value of x in this domain Case 3: When 1<x<2 (x−1)−(x−2)−(x−3)≥6 x≤−2 Therefore, no possible value of x in this domain. Case 3: When x<1 −(x−1)−(x−2)−(x−3)≥6 x≤0 Therefore, the value of x∊(−∞,0] Therefore, the value of x that will satisfy this inequality: x∊(−∞,0]∪[4,∞) Hence, option B is the correct answer.