138 Решите уравнение: а) \(\frac{2(x - 3)}{3} + \frac{5(x - 3)}{27} = 46\); б) \(\frac{5(7x - 2)}{2} - \frac{9(2x + 8)}{4} = 5x + 1\); в) \(2\frac{2}{5} \cdot (2x + 9) + \frac{3}{25} \cdot (5x - 10) = \frac{3}{5} \cdot (6x - 5)\); г) \(\frac{3}{7} \cdot (3x - 1) - \frac{4}{21} \cdot (6x + 5) = \frac{5}{21} \cdot (4x + 1)\).

Решение: а) \(\frac{2(x - 3)}{3} + \frac{5(x - 3)}{27} = 46\). Умножим обе части уравнения на 27: \(2 \cdot 9(x - 3) + 5(x - 3) = 46 \cdot 27\) \(18(x - 3) + 5(x - 3) = 1242\) \(18x - 54 + 5x - 15 = 1242\) \(23x - 69 = 1242\) \(23x = 1311\) \(x = \frac{1311}{23}\) \(x = 57\)

б) \(\frac{5(7x - 2)}{2} - \frac{9(2x + 8)}{4} = 5x + 1\). Умножим обе части уравнения на 4: \(2 \cdot 5(7x - 2) - 9(2x + 8) = 4(5x + 1)\) \(10(7x - 2) - 9(2x + 8) = 20x + 4\) \(70x - 20 - 18x - 72 = 20x + 4\) \(52x - 92 = 20x + 4\) \(32x = 96\) \(x = 3\)

в) \(2\frac{2}{5} \cdot (2x + 9) + \frac{3}{25} \cdot (5x - 10) = \frac{3}{5} \cdot (6x - 5)\). \(\frac{12}{5} (2x + 9) + \frac{3}{25}(5x - 10) = \frac{3}{5}(6x - 5)\) Умножим обе части уравнения на 25: \(5 \cdot 12 (2x + 9) + 3(5x - 10) = 5 \cdot 3(6x - 5)\) \(60(2x + 9) + 3(5x - 10) = 15(6x - 5)\) \(120x + 540 + 15x - 30 = 90x - 75\) \(135x + 510 = 90x - 75\) \(45x = -585\) \(x = -13\)

г) \(\frac{3}{7} \cdot (3x - 1) - \frac{4}{21} \cdot (6x + 5) = \frac{5}{21} \cdot (4x + 1)\). Умножим обе части уравнения на 21: \(3 \cdot 3(3x - 1) - 4(6x + 5) = 5(4x + 1)\) \(9(3x - 1) - 4(6x + 5) = 5(4x + 1)\) \(27x - 9 - 24x - 20 = 20x + 5\) \(3x - 29 = 20x + 5\) \(-17x = 34\) \(x = -2\)

Ответ: а) x = 57; б) x = 3; в) x = -13; г) x = -2.