For what value of n is |n − 1| + 1 equal to 0 ?

Choice D is correct. If the value of |n - 1| + 1= 0, then |n - 1| + 1 = 0. Subtracting 1 from both sides of this equation gives |n-1| = -1. The expression |n -1| on the left side of the equation is the absolute value of n - 1, and the absolute value of a quantity can never be negative. Thus |n - 1| = -1 has no solution. Therefore, there are no values for n for which the value of |n - 1| + 1 is equal to 0.
Choice A is incorrect because |0 - 1| + 1 = 1 + 1 = 2, not 0. Choice B is incorrect because |1 - 1| + 1 = 0 + 1 = 1, not 0. Choice C is incorrect because |2 - 1| + 1 = 1 + 1 = 2, not 0.