Final Answer:
C) 4146 < x < 4156
Step-by-step explanation:
The solution set for the inequality |x₋₄₁₅₁| can be determined by considering two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: x - 4151 ≥ 0
If x - 4151 ≥ 0, then |x₋₄₁₅₁| = x - 4151. Solving for x in this case yields x ≥ 4151.
Case 2: x - 4151 < 0
If x - 4151 < 0, then |x₋₄₁₅₁| = -(x - 4151). Solving for x in this case results in x < 4151.
Combining both cases, the solution set for the inequality is 4151 ≤ x < 4156. However, since the question asks for the solution in terms of strict inequalities, the final answer is 4146 < x < 4156.
In summary, the solution set for the inequality |x₋₄₁₅₁| is 4146 < x < 4156. This means that x must be greater than 4146 but less than 4156 to satisfy the given inequality.