5. Решите уравнение: 3x+2 x-4 1) -4=2; 12 8 2) (6x+1)(3x + 2) = (9x-1)(2x + 5) – 3x.

1) $$ \frac{3x+2}{12} - \frac{x-4}{8} = 2 $$

Общий знаменатель 24, тогда:

$$ \frac{2(3x+2) - 3(x-4)}{24} = \frac{48}{24} $$

2(3x + 2) - 3(x - 4) = 48

6x + 4 - 3x + 12 = 48

3x + 16 = 48

3x = 32

$$ x = \frac{32}{3} = 10 \frac{2}{3} $$

2) (6x+1)(3x + 2) = (9x-1)(2x + 5) – 3x

18x² + 12x + 3x + 2 = 18x² + 45x - 2x - 5 - 3x

18x² + 15x + 2 = 18x² + 40x - 5

18x² + 15x + 2 - 18x² - 40x + 5 = 0

-25x + 7 = 0

-25x = -7

$$ x = \frac{7}{25} = 0.28 $$

Ответ: 1) $$ x = 10\frac{2}{3} $$, 2) $$ x = 0.28 $$