200. Решите уравнение: 1) 4x = 24 + x; 2) 8x - 8 = 20 – 6x; 3) 9 - 4x = 3x – 40; 4) 0,6x – 5,4 = -0,8x + 5,8; 5) 4,7 - 1,1x = 0,5x - 3,3; 6) \frac{5}{6}x+16 = \frac{4}{9}x+9. 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 уравнений: 200. Решите уравнение: 1) $$4x = 24 + x$$ $$4x - x = 24$$ $$3x = 24$$ $$x = \frac{24}{3}$$ $$\bold{x = 8}$$ 2) $$8x - 8 = 20 - 6x$$ $$8x + 6x = 20 + 8$$ $$14x = 28$$ $$x = \frac{28}{14}$$ $$\bold{x = 2}$$ 3) $$9 - 4x = 3x - 40$$ $$-4x - 3x = -40 - 9$$ $$-7x = -49$$ $$x = \frac{-49}{-7}$$ $$\bold{x = 7}$$ 4) $$0,6x - 5,4 = -0,8x + 5,8$$ $$0,6x + 0,8x = 5,8 + 5,4$$ $$1,4x = 11,2$$ $$x = \frac{11,2}{1,4}$$ $$\bold{x = 8}$$ 5) $$4,7 - 1,1x = 0,5x - 3,3$$ $$-1,1x - 0,5x = -3,3 - 4,7$$ $$-1,6x = -8$$ $$x = \frac{-8}{-1,6}$$ $$\bold{x = 5}$$ 6) $$\frac{5}{6}x + 16 = \frac{4}{9}x + 9$$ $$\frac{5}{6}x - \frac{4}{9}x = 9 - 16$$ $$\frac{15}{18}x - \frac{8}{18}x = -7$$ $$\frac{7}{18}x = -7$$ $$x = -7 \cdot \frac{18}{7}$$ $$\bold{x = -18}$$ 201. Найдите корень уравнения: 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) $$2,7 + 3y = 9(y - 2,1)$$ $$2,7 + 3y = 9y - 18,9$$ $$3y - 9y = -18,9 - 2,7$$ $$-6y = -21,6$$ $$y = \frac{-21,6}{-6}$$ $$\bold{y = 3,6}$$ 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) $$\frac{5}{6}(\frac{1}{3}x - \frac{1}{5}) = 3x + 3\frac{1}{3}$$ $$\frac{5}{6}(\frac{1}{3}x - \frac{1}{5}) = 3x + \frac{10}{3}$$ $$\frac{5}{18}x - \frac{1}{6} = 3x + \frac{10}{3}$$ $$\frac{5}{18}x - 3x = \frac{10}{3} + \frac{1}{6}$$ $$\frac{5}{18}x - \frac{54}{18}x = \frac{20}{6} + \frac{1}{6}$$ $$-\frac{49}{18}x = \frac{21}{6}$$ $$x = \frac{21}{6} \cdot (-\frac{18}{49})$$ $$x = \frac{7}{2} \cdot (-\frac{6}{49})$$ $$x = \frac{1}{1} \cdot (-\frac{3}{7})$$ $$\bold{x = -\frac{3}{7}}$$