Решите уравнения-пропорции: \(\frac{5x-1}{3} = \frac{3}{2}\), \(\frac{3}{x+3} = \frac{2}{x-2}\), \(\frac{18}{x} = 2x\)

Решение:

1. \(\frac{5x-1}{3} = \frac{3}{2}\)

1. Крест-накрест: \( (5x-1) \cdot 2 = 3 \cdot 3 \)
2. \( 10x - 2 = 9 \)
3. \( 10x = 9 + 2 \)
4. \( 10x = 11 \)
5. \( x = \frac{11}{10} = 1.1 \)

2. \(\frac{3}{x+3} = \frac{2}{x-2}\)

1. Крест-накрест: \( 3(x-2) = 2(x+3) \)
2. \( 3x - 6 = 2x + 6 \)
3. \( 3x - 2x = 6 + 6 \)
4. \( x = 12 \)

3. \(\frac{18}{x} = 2x\)

1. Умножим обе части на \( x \) (при условии \( x \neq 0 \)): \( 18 = 2x^2 \)
2. \( x^2 = \frac{18}{2} \)
3. \( x^2 = 9 \)
4. \( x = \pm \sqrt{9} \)
5. \( x = \pm 3 \)

Ответ: \(x = 1.1\), \(x = 12\), \(x = \pm 3\).