365. Найдите корень уравнения: a) 2,442 : (6,8 – x) = 8,14; б) 3,6 * (1,3 + y) = 7,56; в) 0,3n + 1,6n – 0,31 = 0,45; г) 8,3m - 4m - 1,8m + 4,25 = 8.

Решение: a) \[ \begin{aligned} 2.442 : (6.8 - x) &= 8.14 \\ 6.8 - x &= \frac{2.442}{8.14} \\ 6.8 - x &= 0.3 \\ x &= 6.8 - 0.3 \\ x &= 6.5 \end{aligned} \] Ответ: x = 6.5 б) \[ \begin{aligned} 3.6 \cdot (1.3 + y) &= 7.56 \\ 1.3 + y &= \frac{7.56}{3.6} \\ 1.3 + y &= 2.1 \\ y &= 2.1 - 1.3 \\ y &= 0.8 \end{aligned} \] Ответ: y = 0.8 в) \[ \begin{aligned} 0.3n + 1.6n - 0.31 &= 0.45 \\ 1.9n &= 0.45 + 0.31 \\ 1.9n &= 0.76 \\ n &= \frac{0.76}{1.9} \\ n &= 0.4 \end{aligned} \] Ответ: n = 0.4 г) \[ \begin{aligned} 8.3m - 4m - 1.8m + 4.25 &= 8 \\ (8.3 - 4 - 1.8)m &= 8 - 4.25 \\ 2.5m &= 3.75 \\ m &= \frac{3.75}{2.5} \\ m &= 1.5 \end{aligned} \] Ответ: m = 1.5