Given 2x − 13 − 1 ≥ x − 5 − 3x2, find the maximum and minimum of | X-1 | - | x + 3 |

Given 2x − 13 − 1 ≥ x − 5 − 3x2, find the maximum and minimum of | X-1 | - | x + 3 |

If we remove the denominator, we can get 2 (2x-1) - 6 ≥ 6x-3 (5-3x), remove the bracket, we can get 4x-2-6 ≥ 6x-15 + 9x, shift the term, we can get 4x-6x-9x ≥ - 15 + 2 + 6, merge the similar terms, we can get: - 11x ≥ - 7 ∧ solve the inequality system, we can get x ≤ 711 (1) when - 3 ≤ x ≤ 711, | X-1 | - | x + 3 | = - (2 + 2x), when x = 711, we can get the minimum value of - 3611; (2) when x ＜ - 3, | X-1 | - | x + 3 | we can get 1-x + X + 3 = 4 (maximum value)