5. Решите уравнение: 1) 6x-1_x+1=1; 14 4 2) (3x+1)(5x - 1) = (5x + 2)(3x-4) - 7x.

1) $$ \frac{6x-1}{14} - \frac{x+1}{4} = 1 $$

Общий знаменатель 28, тогда:

$$ \frac{2(6x-1) - 7(x+1)}{28} = \frac{28}{28} $$

$$ 2(6x - 1) - 7(x + 1) = 28 $$

$$ 12x - 2 - 7x - 7 = 28 $$

$$ 5x - 9 = 28 $$

$$ 5x = 37 $$

$$ x = \frac{37}{5} = 7.4 $$

2) (3x+1)(5x - 1) = (5x + 2)(3x-4) - 7x

15x² - 3x + 5x - 1 = 15x² - 20x + 6x - 8 - 7x

15x² + 2x - 1 = 15x² - 21x - 8

15x² + 2x - 1 - 15x² + 21x + 8 = 0

23x + 7 = 0

23x = -7

$$ x = - \frac{7}{23} $$

Ответ: 1) $$ x = 7.4 $$, 2) $$ x = -\frac{7}{23} $$