Задание 2. Найдите корень уравнения. 1) x---34; 189 2)-5++; 3) +1=; 4) -. 5). 5-2; x+9=-2; 6) 5-12 x-5

Задание 2. Найдите корень уравнения.

1) $$x - \frac{x}{18} = -\frac{34}{9}$$

$$\frac{18x - x}{18} = -\frac{34}{9}$$

$$\frac{17x}{18} = -\frac{34}{9}$$

$$x = -\frac{34}{9} \cdot \frac{18}{17} = -\frac{2}{1} \cdot \frac{2}{1} = -4$$

Ответ: -4

2) $$-5 + \frac{x}{3} = \frac{x + 8}{6}$$

$$\frac{x}{3} - \frac{x + 8}{6} = 5$$

$$\frac{2x - (x + 8)}{6} = 5$$

$$\frac{2x - x - 8}{6} = 5$$

$$\frac{x - 8}{6} = 5$$

$$x - 8 = 30$$

$$x = 30 + 8$$

$$x = 38$$

Ответ: 38

3) $$\frac{7x + 2}{4} + 1 = \frac{5x}{3}$$

$$\frac{7x + 2}{4} - \frac{5x}{3} = -1$$

$$\frac{3(7x + 2) - 4(5x)}{12} = -1$$

$$\frac{21x + 6 - 20x}{12} = -1$$

$$\frac{x + 6}{12} = -1$$

$$x + 6 = -12$$

$$x = -12 - 6$$

$$x = -18$$

Ответ: -18

4) $$\frac{16}{x + 3} = \frac{8}{11}$$

$$8(x + 3) = 16 \cdot 11$$

$$8x + 24 = 176$$

$$8x = 176 - 24$$

$$8x = 152$$

$$x = \frac{152}{8} = 19$$

Ответ: 19

5) $$\frac{5}{x + 9} = -2$$

$$-2(x + 9) = 5$$

$$-2x - 18 = 5$$

$$-2x = 5 + 18$$

$$-2x = 23$$

$$x = -\frac{23}{2} = -11,5$$

Ответ: -11,5

6) $$\frac{5}{x - 12} = \frac{12}{x - 5}$$

$$12(x - 12) = 5(x - 5)$$

$$12x - 144 = 5x - 25$$

$$12x - 5x = -25 + 144$$

$$7x = 119$$

$$x = \frac{119}{7} = 17$$

Ответ: 17