3 Задача: Найдите корень уравнения. a) -40(x - 15) = -200 г) (4,2 - 0,3x)3,5 = 14 6) (20-8x)5 = 220 д) (6x - 2,8)8 = 22, 4 в) 7/5 x - 3/14 = 1/7 e) 2/5 x + 3/10 x = 4,5

Решение:

1. а) -40(x - 15) = -200
   \( x - 15 = \frac{-200}{-40} \)
   \( x - 15 = 5 \)
   \( x = 5 + 15 \)
   \( x = 20 \)
2. б) (20 - 8x)5 = 220
   \( 20 - 8x = \frac{220}{5} \)
   \( 20 - 8x = 44 \)
   \( -8x = 44 - 20 \)
   \( -8x = 24 \)
   \( x = \frac{24}{-8} \)
   \( x = -3 \)
3. в) $$\frac{7}{5}x - \frac{3}{14} = \frac{1}{7}$$
   \( \frac{7}{5}x = \frac{1}{7} + \frac{3}{14} \)
   \( \frac{7}{5}x = \frac{2}{14} + \frac{3}{14} \)
   \( \frac{7}{5}x = \frac{5}{14} \)
   \( x = \frac{5}{14} \cdot \frac{5}{7} \)
   \( x = \frac{25}{98} \)
4. г) (4,2 - 0,3x)3,5 = 14
   \( 4.2 - 0.3x = \frac{14}{3.5} \)
   \( 4.2 - 0.3x = 4 \)
   \( -0.3x = 4 - 4.2 \)
   \( -0.3x = -0.2 \)
   \( x = \frac{-0.2}{-0.3} \)
   \( x = \frac{2}{3} \)
5. д) (6x - 2,8)8 = 22, 4
   \( 6x - 2.8 = \frac{22.4}{8} \)
   \( 6x - 2.8 = 2.8 \)
   \( 6x = 2.8 + 2.8 \)
   \( 6x = 5.6 \)
   \( x = \frac{5.6}{6} \)
   \( x = \frac{56}{60} \)
   \( x = \frac{14}{15} \)
6. е) $$\frac{2}{5}x + \frac{3}{10}x = 4,5$$
   \( \frac{4}{10}x + \frac{3}{10}x = 4.5 \)
   \( \frac{7}{10}x = 4.5 \)
   \( x = 4.5 \cdot \frac{10}{7} \)
   \( x = \frac{45}{7} \)

Ответ: а) x = 20; б) x = -3; в) x = 25/98; г) x = 2/3; д) x = 14/15; е) x = 45/7.