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

a) 11,4b − (2,7b + 3,2b) + 2,35 = 6,2;

11,4b - 5,9b + 2,35 = 6,2;

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

5,5b = 3,85;

b = 3,85 / 5,5;

b = 0,7.

б) 15d − (12,1d − 0,7d) + 5,6 = 20;

15d - 11,4d + 5,6 = 20;

3,6d = 20 - 5,6;

3,6d = 14,4;

d = 14,4 / 3,6;

d = 4.

в) 3x + 1/6 − (3 1/2 x − 1 1/4 x) = 4 2/3

$$3x + \frac{1}{6} - (\frac{7}{2}x - \frac{5}{4}x) = \frac{14}{3}$$

$$3x + \frac{1}{6} - \frac{9}{4}x = \frac{14}{3}$$

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

$$\frac{3}{4}x = \frac{28-1}{6}$$

$$\frac{3}{4}x = \frac{27}{6}$$

$$\frac{3}{4}x = \frac{9}{2}$$

$$x = \frac{9}{2} \cdot \frac{4}{3}$$

$$x = 6$$

Ответ: a) b = 0,7; б) d = 4; в) x = 6.