Решить неравенство: |x-1| + |x+2| ≤3

| x - 1 | + | x + 2 | ≤ 3;

| x - 1 | + ≤ 3 - | x + 2 |;

{ x - 1 = ≤ 3 - | x + 2 |, - (x - 1) ≤ 3 - | x + 2 |;

{ x - 1 - 3 = ≤ - | x + 2 |, - x + 1 - 3 ≤ - | x + 2 |;

{ x - 4 = ≤ - | x + 2 |, - x - 2 ≤ - | x + 2 |;

Отсюда:

1) x - 4 = ≤ - (x + 2);

x - 4 < = - x - 2;

x + x < = - 2 + 4;

2 * x < = 2;

x < = 1;

2) - (x - 4) = ≤ - (x + 2);

- x + 4 < = - x - 2;

- x + x < = - 2 - 4;

Нет решения;

3) - x - 2 ≤ - (x + 2);

- x - 2 < = - x - 2;

- x + x < = - 2 + 2;

Нет решения;

4) - ( - x - 2) ≤ - (x + 2);

x + 2 < = - x - 2;

x + x < = - 2 - 2;

2 * x < = - 4;

x < = - 4 / 2;

x < = - 2;

Объединяя, x < = 1 и x < = - 2 получим: x < = - 2.