Calcula x en las siguientes proporciones:

Solución:

1. a) \( \frac{6}{9} = \frac{10}{x} \)
   \( 6x = 9 \times 10 \)
   \( 6x = 90 \)
   \( x = \frac{90}{6} \)
   \( x = 15 \)
2. b) \( \frac{6}{4} = \frac{x}{6} \)
   \( 4x = 6 \times 6 \)
   \( 4x = 36 \)
   \( x = \frac{36}{4} \)
   \( x = 9 \)
3. c) \( \frac{8}{x} = \frac{12}{15} \)
   \( 12x = 8 \times 15 \)
   \( 12x = 120 \)
   \( x = \frac{120}{12} \)
   \( x = 10 \)
4. d) \( \frac{x}{21} = \frac{4}{28} \)
   \( 28x = 21 \times 4 \)
   \( 28x = 84 \)
   \( x = \frac{84}{28} \)
   \( x = 3 \)
5. e) \( \frac{x}{39} = \frac{30}{65} \)
   \( 65x = 39 \times 30 \)
   \( 65x = 1170 \)
   \( x = \frac{1170}{65} \)
   \( x = 18 \)
6. f) \( \frac{14}{x} = \frac{49}{42} \)
   \( 49x = 14 \times 42 \)
   \( 49x = 588 \)
   \( x = \frac{588}{49} \)
   \( x = 12 \)
7. g) \( \frac{15}{24} = \frac{55}{x} \)
   \( 15x = 24 \times 55 \)
   \( 15x = 1320 \)
   \( x = \frac{1320}{15} \)
   \( x = 88 \)
8. h) \( \frac{42}{54} = \frac{x}{63} \)
   \( 54x = 42 \times 63 \)
   \( 54x = 2646 \)
   \( x = \frac{2646}{54} \)
   \( x = 49 \)
9. i) \( \frac{16}{x} = \frac{32}{16} \)
   \( 32x = 16 \times 16 \)
   \( 32x = 256 \)
   \( x = \frac{256}{32} \)
   \( x = 8 \)

Ответ: a) x = 15; b) x = 9; c) x = 10; d) x = 3; e) x = 18; f) x = 12; g) x = 88; h) x = 49; i) x = 8.