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

a) \(\frac{x - 4}{8} = \frac{7}{4}\);

Решим пропорцию:

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

\(4x - 16 = 56\)

\(4x = 56 + 16\)

\(4x = 72\)

\(x = \frac{72}{4}\)

\(x = 18\)

Ответ: 18

---

б) \(\frac{5}{3x + 2} = \frac{2,5}{27,5}\);

Решим пропорцию:

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

\(7,5x + 5 = 137,5\)

\(7,5x = 137,5 - 5\)

\(7,5x = 132,5\)

\(x = \frac{132,5}{7,5}\)

\(x = \frac{1325}{75}\)

\(x = \frac{53}{3} = 17\frac{2}{3}\)

Ответ: \(17\frac{2}{3}\)

---

B) \(\frac{x + 6}{4} = \frac{2x - 15}{7}\);

Решим пропорцию:

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

\(7x + 42 = 8x - 60\)

\(7x - 8x = -60 - 42\)

\(-x = -102\)

\(x = 102\)

Ответ: 102

---

г) \(\frac{0,3}{x + 5} = \frac{0,8}{x - 9}\).

Решим пропорцию:

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

\(0,3x - 2,7 = 0,8x + 4\)

\(0,3x - 0,8x = 4 + 2,7\)

\(-0,5x = 6,7\)

\(x = \frac{6,7}{-0,5}\)

\(x = -13,4\)

Ответ: -13,4