The solution set of inequality | X-1 | + | X-2 | > 3 is______ ．

The solution set of inequality | X-1 | + | X-2 | > 3 is______ ．

Because | X-1 | + | X-2 | represents the sum of the distances from the corresponding points of X to the corresponding points of 1 and 2 on the number axis, and the sum of the distances from the corresponding points of 0 and 3 to the corresponding points of 1 and 2 is equal to 3, the inequality | X-1 | + | X-2 | > 3 holds when x ＜ 1 or X ＞ 3. Therefore, the solution set of the inequality | X-1 | + | X-2 | > 3 is (- ∞, 0) ∪ (3, + ∞), so the answer is (- ∞, 0) ∪ (3, + ∞)