The expression is in the form ||a| - 2| = 1
There are 4 possibilities, when trying to solve this equation
|-a -2| = 1There are 2 options:
-(-a -2) = 1 => a +2 = 1 => a = -1
(-a - 2) = 1 => -a = 3 => a = -3
|a - 2| = 1There are 2 options:
-(a - 2) = 1 => -a + 2 = 1 => a = 1
(a - 2) = 1 => a = 3
Hence, there are 4 values for a which are -3,-1,1,3
Coming back to the question, if we substitute a to be x-1
x - 1 = -3 => x = -2
x - 1 = -1 => x = 0
x - 1 = 1 => x = 2
x - 1 = 3 => x = 4
Hence, the range of the values is
6(Option D)
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