It is known that: | X-1 | + | X-5 | = 4, then the value range of X is () A. 1≤x≤5B. x≤1C. 1<x<5D. x≥5

It is known that: | X-1 | + | X-5 | = 4, then the value range of X is () A. 1≤x≤5B. x≤1C. 1<x<5D. x≥5

Consider from three cases: first, when x ≥ 5, the original equation can be reduced to: X-1 + X-5 = 4, the solution is: x = 5; second, when 1 < x < 5, the original equation can be reduced to: x-1-x + 5 = 4, the constant holds; third, when x ≤ 1, the original equation can be reduced to: - x + 1-x + 5 = 4, the solution is: x = 1; so the value range of X is: 1 ≤ x ≤ 5