201. Найдите корень уравнения: 1) 4(x - 3) = x + 6; 2) 4 - 6(x + 2) = 3 - 5x; 3) (5x + 8) - (8x + 14) = 9; 4) 2,7 + 3y = 9(y – 2,1); 5) 0,3(8 - 3y) = 3,2 – 0,8(y – 7); 6) \frac{5}{6}(\frac{1}{3}x - \frac{1}{5}) = 3x + 3\frac{1}{3}.

Решение уравнений:

1) \(4(x - 3) = x + 6\)

\[4x - 12 = x + 6\] \[4x - x = 6 + 12\] \[3x = 18\] \[x = 6\]

Ответ: \(x = 6\)

2) \(4 - 6(x + 2) = 3 - 5x\)

\[4 - 6x - 12 = 3 - 5x\] \[-6x + 5x = 3 - 4 + 12\] \[-x = 11\] \[x = -11\]

Ответ: \(x = -11\)

3) \((5x + 8) - (8x + 14) = 9\)

\[5x + 8 - 8x - 14 = 9\] \[5x - 8x = 9 - 8 + 14\] \[-3x = 15\] \[x = -5\]

Ответ: \(x = -5\)

4) \(2,7 + 3y = 9(y - 2,1)\)

\[2,7 + 3y = 9y - 18,9\] \[3y - 9y = -18,9 - 2,7\] \[-6y = -21,6\] \[y = 3,6\]

Ответ: \(y = 3,6\)

5) \(0,3(8 - 3y) = 3,2 - 0,8(y - 7)\)

\[2,4 - 0,9y = 3,2 - 0,8y + 5,6\] \[-0,9y + 0,8y = 3,2 + 5,6 - 2,4\] \[-0,1y = 6,4\] \[y = -64\]

Ответ: \(y = -64\)

6) \(\frac{5}{6}(\frac{1}{3}x - \frac{1}{5}) = 3x + 3\frac{1}{3}\)

\[\frac{5}{6}(\frac{1}{3}x - \frac{1}{5}) = 3x + \frac{10}{3}\] \[\frac{5}{18}x - \frac{5}{30} = 3x + \frac{10}{3}\] \[\frac{5}{18}x - \frac{1}{6} = 3x + \frac{10}{3}\] \[\frac{5}{18}x - 3x = \frac{10}{3} + \frac{1}{6}\] \[\frac{5}{18}x - \frac{54}{18}x = \frac{10 \cdot 2}{3 \cdot 2} + \frac{1}{6}\] \[-\frac{49}{18}x = \frac{20}{6} + \frac{1}{6}\] \[-\frac{49}{18}x = \frac{21}{6}\] \[x = \frac{21}{6} \cdot (-\frac{18}{49})\] \[x = \frac{3}{1} \cdot (-\frac{3}{7})\] \[x = -\frac{9}{7}\] \[x = -1\frac{2}{7}\]

Ответ: \(x = -1\frac{2}{7}\)