Решите уравнения с модулями 9-x=|3x+1| |x-7|=-2 |2x-1|=|x+3|=8 |x-3|+|x+2|-|x-4|=3 решите неравенства |1-2x|>3-x |x-3|<1 |x-2|+|x+5<=7

1. 9-x=|3x+1|;

1) 9 - x = 3 * x + 1;

- x - 3 * x = 1 - 9;

- 4 * x = - 8;

x = 8 / 4;

x = 2;

2) 9 - x = - 3 * x - 1;

- x + 3 * x = - 1 - 9;

2 * x = - 10;

x = - 10 / 2;

x = - 5;

Ответ: х = 2 и х = - 5.

2. |x-7|=-2;

1) x - 7 = - 2;

x = - 2 + 7;

x = 5;

2) - (x - 7) = - 2;

x - 7 = 2;

x = 2 + 7;

x = 9;

Ответ: х 5 и х = 9.

3. |2x-1|+|x+3|=8;

1) 2 * x - 1 + x + 3 = 8;

3 * x + 2 = 8;

3 * x = 6;

x = 2;

2) - 2 * x + 1 - x - 3 = 8;

- 3 * x - 2 = 8;

- 3 * x = 10;

x = - 10 / 3;

Ответ: х = 2 и х = - 10 / 3.

4. |x-3|+|x+2|-|x-4|=3;

1) X - 3 + X + 2 - X + 4 = 3;

X - 3 = 3;

X = 6;

2) x - 3 + x + 2 - x + 4 = - 3;

x - 3 = - 3;

x = 0;

Ответ: х = 6 и х = 0.

5. |1-2x|>3-x;

{ 1 - 2 x > 3 - x, - (1 - 2 x) > 3 - x;

{ - 2 x + x > 3 - 1, 2 x + x > 3 + 1;

{ - x > 2, 3 x > 4;

{ x 4 / 3;

6. |x-3|<1;

{ x - 3 < 1, - x + 3 < 1;

{ x < 4, - x < - 2;

{ x 2;

{ 2 < x < 4;

7. |x-2|+|x+5<=7;

{ x - 2 + x + 5 = - 7;

{ 2 * x = - 10;

{ x = - 5;

{ - 5 < = x < = 2.