1150. Решите уравнение: 1) 0,4(x - 3) - 1,6 = 5(0,1x – 0,5); 2) 1,5(2x - 5) + 2x = 5(0,5x - 1,5) – 10; 3) \(\frac{2}{3}\left(1\frac{1}{2}x + \frac{3}{5}\right) - \frac{4}{5}\left(\frac{5}{12}x - \frac{1}{2}\right) = 1\frac{3}{5}\)

Решение:

1. \(0,4(x - 3) - 1,6 = 5(0,1x – 0,5) \)
   \(0,4x - 1,2 - 1,6 = 0,5x - 2,5 \)
   \(0,4x - 2,8 = 0,5x - 2,5 \)
   \(-2,8 + 2,5 = 0,5x - 0,4x \)
   \(-0,3 = 0,1x \)
   \(x = \frac{-0,3}{0,1} \)
   \(x = -3 \)
2. \(1,5(2x - 5) + 2x = 5(0,5x - 1,5) – 10 \)
   \(3x - 7,5 + 2x = 2,5x - 7,5 - 10 \)
   \(5x - 7,5 = 2,5x - 17,5 \)
   \(5x - 2,5x = -17,5 + 7,5 \)
   \(2,5x = -10 \)
   \(x = \frac{-10}{2,5} \)
   \(x = -4 \)
3. \(\frac{2}{3}\left(1\frac{1}{2}x + \frac{3}{5}\right) - \frac{4}{5}\left(\frac{5}{12}x - \frac{1}{2}\right) = 1\frac{3}{5}\)
   \(\frac{2}{3}\left(\frac{3}{2}x + \frac{3}{5}\right) - \frac{4}{5}\left(\frac{5}{12}x - \frac{1}{2}\right) = \frac{8}{5}\)
   \(\left(\frac{2}{3} \cdot \frac{3}{2}x\right) + \left(\frac{2}{3} \cdot \frac{3}{5}\right) - \left(\frac{4}{5} \cdot \frac{5}{12}x\right) + \left(\frac{4}{5} \cdot \frac{1}{2}\right) = \frac{8}{5}\)
   \(x + \frac{2}{5} - \frac{1}{3}x + \frac{2}{5} = \frac{8}{5}\)
   \(x - \frac{1}{3}x + \frac{4}{5} = \frac{8}{5}\)
   \(\frac{2}{3}x = \frac{8}{5} - \frac{4}{5}\)
   \(\frac{2}{3}x = \frac{4}{5}\)
   \(x = \frac{4}{5} \cdot \frac{3}{2}\)
   \(x = \frac{12}{10}\)
   \(x = 1\frac{1}{5} \)

Ответ: 1) x = -3; 2) x = -4; 3) x = 1\(\frac{1}{5}\).