Question

If $x$ satisfies $|x-1|+|x-2|+|x-3|\ge 6$, then

• A. $0\le x\le 4$
• B. $x\le -2$ or $x\ge 4$
• C. $x\le 0$ or $x\ge 4$
• D. None of these

Answer 1

The correct option is C $x\le 0$ or $x\ge 4$

Let $|x-1|+|x-2|+|x-3|<6$
or, $|(x-1)+(x-2)+(x-3)|<|x-1|+|x-2|+|x-3|<6$
or, $|3x-6|<6$
or, $|x-2|<2$
or, $-2<x-2<2$
or, $0<x<4$
Therefore, for $|x-1|+|x-2|+|x-3|\ge 6,x\le 0$ or $x\ge 4$