A) \[0\le x\le 4\]
B) \[x\le -2\]and \[x\le 4\]
C) \[x\le 0\]and\[x\ge 4\]
D) None of these
Correct Answer: C
Solution :
\[|x-1|+|x-2|+|x-3|\ge 6\] For \[x<1,\] \[-(x-1)-(x-2)-(x-3)\ge 6\] \[\Rightarrow \] \[-3x+6\ge 6\] \[\Rightarrow \] \[-3x\ge 0\] \[\Rightarrow \] \[x\le 0\] ...(i) For \[1\le x<2,\] \[(x-1)-(x-2)-(x-3)\ge 6\] \[\Rightarrow \] \[x-1-x+2-x+3\ge 6\] \[\Rightarrow \] \[-x+4\ge 6\] \[\Rightarrow \] \[-x\ge 2\] ...(ii) For\[2\le x<3,\] \[(x-1)+(x-2)-(x-3)\ge 6\] \[\Rightarrow \] \[x\ge 6\] ...(iii) For \[x\ge 3,\] \[x-1+x-2+x-3\ge 6\] \[\Rightarrow \] \[3x-6\ge 6\] \[\Rightarrow \] \[3x\ge 12\] \[\Rightarrow \] \[x\ge 4\] ...(iv) From Eqs. (i), (ii), (iii) and (iv), \[x\le 0\]and \[x\ge 4\]
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