4.318 Найдите х из пропорции: a) \frac{x}{-1,4} = \frac{-7,3}{-2,8}; б) \frac{-8,4}{105} = \frac{-12,6}{x}; в) \frac{-2,5x}{14} = \frac{1}{-\frac{7}{30}}; г) \frac{-7\frac{1}{2}}{4\frac{1}{2}} = \frac{x}{\frac{3}{25}}.

a)\[\frac{x}{-1,4} = \frac{-7,3}{-2,8}\]\[x = \frac{(-1,4) \cdot (-7,3)}{-2,8} = \frac{1,4 \cdot 7,3}{2,8} = \frac{7,3}{2} = 3,65\]

б)\[\frac{-8,4}{105} = \frac{-12,6}{x}\]\[x = \frac{105 \cdot (-12,6)}{-8,4} = \frac{105 \cdot 12,6}{8,4} = \frac{105 \cdot 126}{84} = \frac{105 \cdot 3}{2} = \frac{315}{2} = 157,5\]

в)\[\frac{-2,5x}{14} = \frac{1}{-\frac{7}{30}}\]\[\frac{-2,5x}{14} = -\frac{30}{7}\]\[-2,5x = \frac{14 \cdot (-30)}{7}\]\[-2,5x = -2 \cdot 30\]\[-2,5x = -60\]\[x = \frac{-60}{-2,5} = \frac{60}{2,5} = \frac{600}{25} = 24\]

г)\[\frac{-7\frac{1}{2}}{4\frac{1}{2}} = \frac{x}{\frac{3}{25}}\]\[x = \frac{-7\frac{1}{2} \cdot \frac{3}{25}}{4\frac{1}{2}} = \frac{-\frac{15}{2} \cdot \frac{3}{25}}{\frac{9}{2}} = -\frac{15 \cdot 3 \cdot 2}{2 \cdot 25 \cdot 9} = -\frac{3 \cdot 3 \cdot 2}{2 \cdot 5 \cdot 9} = -\frac{18}{90} = -\frac{1}{5}\]