Y = | 1-x | + | 2-3x | + | - 3-4x | + | - 4-5x | + | - 1-6x | + | - 6-7x |, when y is the minimum value, the value range of X is the minimum value of Y

Y = | 1-x | + | 2-3x | + | - 3-4x | + | - 4-5x | + | - 1-6x | + | - 6-7x |, when y is the minimum value, the value range of X is the minimum value of Y

y=|1-x|+|2-3x|+|3-4x|+|4-5x|+|5-6x|+|6-7x|
Segment discussion:
1. When x ≥ 1
y=x-1+3x-2+4x-3+5x-4+6x-5+7x-6=26x-21
y≥5
2. When 6 / 7 ≤ x ≤ 1
y=-(x-1)+3x-2+4x-3+5x-4+6x-5+7x-6=24x-19
y≥11/7
3. When 5 / 6 ≤ x ≤ 6 / 7
y=-(x-1)+3x-2+4x-3+5x-4+6x-5-(7x-6)=10x-7
y≥4/3
4. When 4 / 5 ≤ x ≤ 5 / 6
y=-(x-1)+3x-2+4x-3+5x-4-(6x-5)-(7x-6)=-2x+3
y≥4/3
5. When 3 / 4 ≤ x ≤ 4 / 5
y=-(x-1)+3x-2+4x-3-(5x-4)-(6x-5)-(7x-6)=-12x+11
y≥7/5
6. When 2 / 3 ≤ x ≤ 3 / 4
y=-(x-1)+3x-2-(4x-3)-(5x-4)-(6x-5)-(7x-6)=-20x+17
y≥2
7. When x ≤ 2 / 3
y=-(x-1)-(3x-2)-(4x-3)-(5x-4)-(6x-5)-(7x-6)=-26x+21
y≥11/3
Therefore, when 3 / 4 ≤ x ≤ 6 / 7, y reaches the minimum
x=5/6,y=4/3