A) 6
B) -1
C) 6 or -1
D) None of these
Correct Answer: C
Solution :
Here \[x=2\] and 3 are the critical points. When \[x<2,|x-2|=-(x-2),|x-3|=-(x-3)\] \[\therefore \]The given equation reduces to \[2-x+3-x=7\] Þ \[x=-1<2\] \ \[x=-1\] is a solution. When \[2\le x<3,\,\,|x-2|=x-2,|x-3|=-(x-3)\] \ The equation reduces to \[x-2+3-x=7\]Þ 1=7 \ No solution in this case. When\[x\ge 3\], the equation reduces to \[x-2+x-3=7\] Þ \[x=6>3\] Hence we get, \[x=6\]or -1 Trick: By inspection, we have that both the values \[x=6,-1\] satisfy the given equation.
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