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Solve `|x-1|-2|=|x-3|`. |
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Answer» Correct Answer - `[1,oo)` `||x-1||-2|=|x-3|` Case I : `x ge 3` `:. |x-1-2|=x-3 implies x-3=x-3` `:.x ge 3` Case II : If `1 le x lt3` `:. |x-1-2|=-(x-3)` `:. -(x-3)=-(x-3)implies1le x lt3` Case III : `-1 le x lt 1` `:, |-x+1-2|=-(x-3)` `:. |-x-1|=-(x-3) implies |x+1|=-x+3` `x+1=-x+3 implies 2x=2impliesx=1` Which is not possible Case IV : IF `x lt -1` `:. |-x+1-2|=-(x-3)` `implies |x+1|=-(x-3)implies-(x+1)=-(x-3)` `implies -x-1=-x+3` `implies` No solution Hence `x in [1,oo)` |
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