A is any rational number. The minimum value of the algebraic formula | A-1 | + | a + 1 | + | a + 2 | is () A. - 1 B.1 C.2 D.3

A is any rational number. The minimum value of the algebraic formula | A-1 | + | a + 1 | + | a + 2 | is () A. - 1 B.1 C.2 D.3

Choose D
This type of problem needs to be solved in geometric sense
First draw a number axis, then the meaning of | A-1 | on the number axis is "the distance between point a and point 1". Similarly, | a + 1 | can be written as | a - (- 1) |, that is, "the distance between point a and point-1", | a + 2 | is "the distance between point a and point-2"
Now the problem is transformed into "find a point a on the number axis to minimize the sum of the distances to point 1, point-1 and point-2."
First, consider the sum of the distances from point a to point-2 and point 1. Only when point a is between point-2 and point 1, the sum of the distances from point a to point-2 and point 1 is the smallest, which is 3. If point a is in other positions, the sum of the distances from point a to point-2 and point 1 will be greater than 3. Then choose a position for point a to make the distance to point-1 the smallest. It is easy to find that when point a is just at point-1, the distance from point a to point-1 is the smallest, which is 0
Therefore, the minimum sum of distances from point a to point - 2, - 1 and point 1 is 3, that is, the minimum value of | A-1 | + | a + 1 | + | a + 2 |, is 3