A) \[-1\]
B) 6
C) \[-1\]or 6
D) None of these
Correct Answer: C
Solution :
Given, \[|x-2|+|x-3|=7\] ...(i) When \[x<2,|x-2|=-(x-2)\] and \[|x-3|=-(x-3)\] Then, from Eq. (i), \[-(x-2)+\{-(x-3)\}=7\] \[\Rightarrow \] \[-x+2-x+3=7\] \[\Rightarrow \] \[-2x=7-5\] \[\Rightarrow \] \[2x=-2\] \[\Rightarrow \] \[x=-1<2\] When \[2\le x<3,|x-2|=(x-2)\] and \[|x-3|=-(x-3),\] Then, from Eq. (i), \[x-2-x+3=7\] \[\Rightarrow \] \[1\ne 7\] So, the solution is not possible. When \[x\ge 3,|x-2|=(x-2)\] and \[|~x-3|=(x-3)\] Then, from Eq. (i), \[x-2+x-3=7\] \[\Rightarrow \] \[2x=7+5\] \[\Rightarrow \] \[x=6>3\] Hence, \[x=6\]or\[-1\]
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