201. Найдите корень уравнения: 1) 4(x - 3) = x + 6; 2) 4 - 6(x + 2) = 3 – 5x; 3) (5x + 8) – (8x + 14) = 9; 4) 2,7 + 3y = 9(y – 2,1); 5) 0,3(8 – 3y) = 3,2 – 0,8(y − 7); 6) $$\frac{5}{6}(\frac{1}{3}x - \frac{1}{5}) = 3x + 3\frac{1}{3}$$.

Решение: 1) $$4(x - 3) = x + 6$$ $$4x - 12 = x + 6$$ $$4x - x = 6 + 12$$ $$3x = 18$$ $$x = \frac{18}{3}$$ $$\bold{x = 6}$$ 2) $$4 - 6(x + 2) = 3 - 5x$$ $$4 - 6x - 12 = 3 - 5x$$ $$-6x + 5x = 3 - 4 + 12$$ $$-x = 11$$ $$\bold{x = -11}$$ 3) $$(5x + 8) - (8x + 14) = 9$$ $$5x + 8 - 8x - 14 = 9$$ $$5x - 8x = 9 - 8 + 14$$ $$-3x = 15$$ $$x = \frac{15}{-3}$$ $$\bold{x = -5}$$ 4) $$2,7 + 3y = 9(y - 2,1)$$ $$2,7 + 3y = 9y - 18,9$$ $$3y - 9y = -18,9 - 2,7$$ $$-6y = -21,6$$ $$y = \frac{-21,6}{-6}$$ $$y = \frac{216}{60}$$ $$y = \frac{36}{10}$$ $$\bold{y = 3,6}$$ 5) $$0,3(8 - 3y) = 3,2 - 0,8(y - 7)$$ $$2,4 - 0,9y = 3,2 - 0,8y + 5,6$$ $$-0,9y + 0,8y = 3,2 + 5,6 - 2,4$$ $$-0,1y = 6,4$$ $$y = \frac{6,4}{-0,1}$$ $$\bold{y = -64}$$ 6) $$\frac{5}{6}(\frac{1}{3}x - \frac{1}{5}) = 3x + 3\frac{1}{3}$$ $$\frac{5}{6}(\frac{1}{3}x - \frac{1}{5}) = 3x + \frac{10}{3}$$ $$\frac{5}{18}x - \frac{5}{30} = 3x + \frac{10}{3}$$ $$\frac{5}{18}x - \frac{1}{6} = 3x + \frac{10}{3}$$ $$\frac{5}{18}x - 3x = \frac{10}{3} + \frac{1}{6}$$ $$\frac{5}{18}x - \frac{54}{18}x = \frac{20}{6} + \frac{1}{6}$$ $$-\frac{49}{18}x = \frac{21}{6}$$ $$-\frac{49}{18}x = \frac{7}{2}$$ $$x = \frac{7}{2} : (-\frac{49}{18})$$ $$x = \frac{7}{2} \cdot (-\frac{18}{49})$$ $$x = -\frac{7 \cdot 18}{2 \cdot 49}$$ $$x = -\frac{126}{98}$$ $$x = -\frac{9}{7}$$ $$\bold{x = -1\frac{2}{7}}$$