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

a)

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

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

\[4x - 16 = 56\]

\[4x = 56 + 16\]

\[4x = 72\]

\[x = \frac{72}{4}\]

\[x = 18\]

в)

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

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

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

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

\[-x = -102\]

\[x = 102\]

б)

\[\frac{5}{3x + 2} = \frac{2,5}{27,5}\]

\[5 \cdot 27,5 = 2,5 (3x + 2)\]

\[137,5 = 7,5x + 5\]

\[7,5x = 137,5 - 5\]

\[7,5x = 132,5\]

\[x = \frac{132,5}{7,5}\]

\[x = \frac{1325}{75}\]

\[x = \frac{53}{3}\]

\[x = 17\frac{2}{3}\]

г)

\[\frac{0,3}{x + 5} = \frac{0,8}{x - 9}\]

\[0,3(x - 9) = 0,8(x + 5)\]

\[0,3x - 2,7 = 0,8x + 4\]

\[0,3x - 0,8x = 4 + 2,7\]

\[-0,5x = 6,7\]

\[x = \frac{6,7}{-0,5}\]

\[x = -13,4\]

Ответ: a) x = 18; в) x = 102; б) x = 17\frac{2}{3}; г) x = -13,4