5.101 Найдите х из пропорции: x - 4 7 a) = 8 4 б) 3x + 2 5 = 27,5 2,5 ; B) x + 6 = 2x - 15; 4 7 0,3 0,8 г) x+5 x-9

Ответ: a) x = 11.5; б) x = 3.5; в) x = 57; г) x = 51

a) \[\frac{x - 4}{8} = \frac{7}{4}\]

\[4(x - 4) = 7 \cdot 8\]

\[4x - 16 = 56\]

\[4x = 72\]

\[x = 18\]

б) \[\frac{3x + 2}{27.5} = \frac{5}{2.5}\]

\[2.5(3x + 2) = 5 \cdot 27.5\]

\[7.5x + 5 = 137.5\]

\[7.5x = 132.5\]

\[x = 17.67\]

в) \[\frac{x + 6}{4} = \frac{2x - 15}{7}\]

\[7(x + 6) = 4(2x - 15)\]

\[7x + 42 = 8x - 60\]

\[x = 102\]

г) \[\frac{0.3}{x + 5} = \frac{0.8}{x - 9}\]

\[0.3(x - 9) = 0.8(x + 5)\]

\[0.3x - 2.7 = 0.8x + 4\]

\[-0.5x = 6.7\]

\[x = -13.4\]

Ответ: a) x = 11.5; б) x = 3.5; в) x = 57; г) x = 51