5.218 Найдите корень уравнения: a) \(\frac{x-11}{15}\) = 16; б) \(\frac{54}{y+7}\) = 6; в) \(\frac{m+6}{11}\) = 4; г) \(\frac{108}{9-c}\) = 9.

а) \(\frac{x-11}{15}\) = 16

x - 11 = 16 ⋅ 15

x - 11 = 240

x = 240 + 11

x = 251

б) \(\frac{54}{y+7}\) = 6

54 = 6(y + 7)

54 = 6y + 42

6y = 54 - 42

6y = 12

y = \(\frac{12}{6}\)

y = 2

в) \(\frac{m+6}{11}\) = 4

m + 6 = 4 ⋅ 11

m + 6 = 44

m = 44 - 6

m = 38

г) \(\frac{108}{9-c}\) = 9

108 = 9(9 - c)

108 = 81 - 9c

9c = 81 - 108

9c = -27

c = \(\frac{-27}{9}\)

c = -3

Ответ: a) x = 251; б) y = 2; в) m = 38; г) c = -3.