X is a rational number, the minimum of | x + 1 | + | X-2 | + | x-3 |. The maximum of | x-3 | - | x + 2 |? | Math enthusiast | Mathematical art

X is a rational number, the minimum of | x + 1 | + | X-2 | + | x-3 |. The maximum of | x-3 | - | x + 2 |?

When x ≤ - 1, | x + 1 | + | X-2 | + | x-3 | = - x-1-x + 2-x + 3 = - 3x + 4, then - 3x + 4 ≥ 7;
When - 1 < x ≤ 2, | x + 1 | + | X-2 | + | x-3 | = x + 1-x + 2-x + 3 = - x + 6, then 4 ≤ - x + 6 < 7;
When 2 ＜ x ≤ 3, | x + 1 | + | X-2 | + | x-3 | = x + 1 + x-2-x + 3 = x + 2, then 4 ＜ x + 2 ≤ 5;
When x > 3, | x + 1 | + | X-2 | + | x-3 | = x + 1 + X-2 + x-3 = 3x-4, then 3x-4 > 5
In conclusion, the minimum value of | x + 1 | + | X-2 | + | x-3 | is 4
When x ≥ 3, the original formula = x-3 - (x + 2) = - 5, the maximum is - 5
When - 2

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