2.314 Найдите корень уравнения: a) 11,4b (2,76 + 3,2b) + 2,35 = 6,2; 6) 15d (12,1d 0,7d) + 5,6 = 20; в) 3х + 1 - 6 - (3х - 1/4) = -4 2/3

a) $$11,4b - (2,7b + 3,2b) + 2,35 = 6,2$$

$$11,4b - 2,7b - 3,2b + 2,35 = 6,2$$

$$5,5b = 6,2 - 2,35$$

$$5,5b = 3,85$$

$$b = \frac{3,85}{5,5} = \frac{385}{550} = \frac{7}{10} = 0,7$$.

б) $$15d - (12,1d - 0,7d) + 5,6 = 20$$

$$15d - 12,1d + 0,7d + 5,6 = 20$$

$$3,6d = 20 - 5,6$$

$$3,6d = 14,4$$

$$d = \frac{14,4}{3,6} = 4$$.

в) $$3x + 1 - 6 - (\frac{3x - 1}{4}) = -4\frac{2}{3}$$

$$3x + 1 - 6 - \frac{3x}{4} + \frac{1}{4} = -\frac{14}{3}$$

$$\frac{12x}{4} - \frac{3x}{4} - 5 + \frac{1}{4} = -\frac{14}{3}$$

$$\frac{9x}{4} = -\frac{14}{3} + 5 - \frac{1}{4}$$

$$\frac{9x}{4} = -\frac{56}{12} + \frac{60}{12} - \frac{3}{12}$$

$$\frac{9x}{4} = \frac{1}{12}$$

$$x = \frac{4}{9 \cdot 12} = \frac{1}{27}$$.

Ответ: а) $$b = 0,7$$, б) $$d = 4$$, в) $$x = \frac{1}{27}$$.