1527. Решите уравнения:

Решение:

1. \( \frac{4x + 23}{5,4} = \frac{8,5}{1,7} \) \( \Rightarrow \frac{4x + 23}{5,4} = 5 \) \( \Rightarrow 4x + 23 = 5 \times 5,4 = 27 \) \( \Rightarrow 4x = 4 \) \( \Rightarrow x = 1 \).
2. \( \frac{5}{6} = \frac{3x + 1,5}{9} \) \( \Rightarrow 5 \times 9 = 6 \times (3x + 1,5) \) \( \Rightarrow 45 = 18x + 9 \) \( \Rightarrow 18x = 36 \) \( \Rightarrow x = 2 \).
3. \( \frac{3}{12} = \frac{1,3x + 2}{2} \) \( \Rightarrow \frac{1}{4} = \frac{1,3x + 2}{2} \) \( \Rightarrow 2 = 4 \times (1,3x + 2) \) \( \Rightarrow 2 = 5,2x + 8 \) \( \Rightarrow 5,2x = -6 \) \( \Rightarrow x = -\frac{6}{5,2} = -\frac{60}{52} = -\frac{15}{13} \).
4. \( \frac{1,4}{2x + 1} = \frac{4,6}{23} \) \( \Rightarrow 1,4 \times 23 = 4,6 \times (2x + 1) \) \( \Rightarrow 32,2 = 9,2x + 4,6 \) \( \Rightarrow 9,2x = 27,6 \) \( \Rightarrow x = 3 \).
5. \( \frac{15}{27} = \frac{9}{8x + 4,2} \) \( \Rightarrow \frac{5}{9} = \frac{9}{8x + 4,2} \) \( \Rightarrow 5 \times (8x + 4,2) = 9 \times 9 \) \( \Rightarrow 40x + 21 = 81 \) \( \Rightarrow 40x = 60 \) \( \Rightarrow x = \frac{60}{40} = 1,5 \).
6. \( \frac{5x - 0,8}{16} = \frac{3,4}{17} \) \( \Rightarrow \frac{5x - 0,8}{16} = 0,2 \) \( \Rightarrow 5x - 0,8 = 16 \times 0,2 = 3,2 \) \( \Rightarrow 5x = 4 \) \( \Rightarrow x = 0,8 \).

Ответ: 1) 1; 2) 2; 3) -\(\frac{15}{13}\); 4) 3; 5) 1,5; 6) 0,8.