If x satisfies the inequality |x-1|+|x-2|+|x-3| ≥ 6

Correct Answer is : x≤0x ≤ 0x≤0 or x≥4x ≥ 4x≥4

Correct Answer is : x≤0x ≤ 0x≤0 or x≥4x ≥ 4x≥4

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Indian Institute of Foreign Trade 2011 Solved Paper

Question : 53 of 120

Marks: +1, -0

|x-1|+|x-2|+|x-3| \ge 6

Solution:

Given that

|x-1|+|x-2|+|x-3|\ge 6

Case 1: When

x > 3

(x-1)+(x-2)+(x-3)\ge 6

x \ge 4

Therefore, the value of

x \in [4,\infty)

Case 2: When

2 < x < 3

(x-1)+(x-2)-(x-3)\ge 6

x \ge 6

Therefore, no possible value of x in this domain

Case 3: When

1 < x < 2

(x-1)-(x-2)-(x-3)\ge 6

x \le -2

Therefore, no possible value of x in this domain.

Case 3: When

x < 1

-(x-1)-(x-2)-(x-3)\ge 6

x \le 0

Therefore, the value of

x \in (-\infty,0]

Therefore, the value of x that will satisfy this inequality:

x \in (-\infty,0] \cup [4,\infty)

Hence, option B is the correct answer.

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