Задание 2. Найдите корень уравнения.

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

$$\frac{18x-x}{18}=-\frac{34}{9}$$ $$\frac{17x}{18}=-\frac{34}{9}$$ $$17x=-\frac{34 \cdot 18}{9}$$ $$17x = -34 \cdot 2$$ $$17x = -68$$ $$x = \frac{-68}{17}$$ $$x = -4$$

Ответ: x = -4

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

$$-\frac{5}{1} + \frac{x}{3} = \frac{x+8}{6}$$ $$-\frac{5 \cdot 6}{1 \cdot 6} + \frac{x \cdot 2}{3 \cdot 2} = \frac{x+8}{6}$$ $$-\frac{30}{6} + \frac{2x}{6} = \frac{x+8}{6}$$ $$-30 + 2x = x + 8$$ $$2x - x = 8 + 30$$ $$x = 38$$

Ответ: x = 38

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

$$\frac{7x+2}{4} + \frac{1}{1} = \frac{5x}{3}$$ $$\frac{3(7x+2) + 1 \cdot 12}{12} = \frac{4 \cdot 5x}{12}$$ $$3(7x+2) + 12 = 20x$$ $$21x + 6 + 12 = 20x$$ $$21x + 18 = 20x$$ $$21x - 20x = -18$$ $$x = -18$$

Ответ: x = -18

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

$$16 \cdot 11 = -8(x+3)$$ $$176 = -8x - 24$$ $$8x = -24 - 176$$ $$8x = -200$$ $$x = \frac{-200}{8}$$ $$x = -25$$

Ответ: x = -25

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

$$5 = -2(x+9)$$ $$5 = -2x - 18$$ $$2x = -18 - 5$$ $$2x = -23$$ $$x = \frac{-23}{2}$$ $$x = -11.5$$

Ответ: x = -11.5

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

$$5(x-5) = 12(x-12)$$ $$5x - 25 = 12x - 144$$ $$5x - 12x = -144 + 25$$ $$-7x = -119$$ $$x = \frac{-119}{-7}$$ $$x = 17$$

Ответ: x = 17