Решите уравнение |х-1|+|х+2|-|х-3|=4

|х - 1| + |х + 2| - |х - 3| = 4;

|х - 1| = 4 - |х + 2| + |х - 3|;

1) x - 1 = 4 - |х + 2| + |х - 3|;

x - 1 - 4 = - |х + 2| + |х - 3|;

x - 5 = - |х + 2| + |х - 3|;

x - 5 + |х + 2| = |х - 3|;

a) x - 3 = x - 5 + |х + 2|;

x - 3 - x + 5 = |х + 2|;

|х + 2| = 2;

x + 2 = 2, x = 2 - 2, x = 0;

x + 2 = - 2, x = - 2 - 2, x = - 4;

б) 3 - x = x - 5 + |х + 2|;

3 - x - х + 5 = |х + 2|;

8 - 2 * х = |х + 2|;

x + 2 = 8 - 2 * x, x + 2 * x = 8 - 2, 3 * x = 6, x = 2;

- x - 2 = 8 - 2 * x, - x + 2 * x = 8 + 2, x = 10;

2) 1 - x = 4 - |х + 2| + |х - 3|;

1 - x - 4 = - |х + 2| + |х - 3|;

- x - 3 + |х + 2| = |х - 3|;

a) x - 3 = - x - 3 + |х + 2|;

x - 3 + x + 3 = + |х + 2|;

2 * x = + |х + 2|;

x + 2 = 2 * x, x = 2;

x + 2 = - 2 * x, x + 2 * x = - 2, 3 * x = - 2, x = - 2 / 3;

б) 3 - х = - x - 3 + |х + 2|;

3 - х + x + 3 = + |х + 2|;

6 = + |х + 2|;

x + 2 = 6, x = 6 - 2, x = 4;

x + 2 = - 6, x = - 6 - 2, x = - 8;

Ответ: х = 0, х = 2, х = 2, х = 10, x = - 2 / 3, x = 4, x = - 8.