Задание 7. Найдите корень уравнения.

Решение:

1. \( \frac{4x+7}{3} + 2 = \frac{7x}{2} \)
   \( \frac{4x+7+6}{3} = \frac{7x}{2} \)
   \( \frac{4x+13}{3} = \frac{7x}{2} \)
   \( 2(4x+13) = 3(7x) \)
   \( 8x + 26 = 21x \)
   \( 26 = 21x - 8x \)
   \( 26 = 13x \)
   \( x = \frac{26}{13} \)
   \( x = 2 \)
2. \( \frac{6x+8}{2} + 5 = \frac{5x}{3} \)
   \( 3x + 4 + 5 = \frac{5x}{3} \)
   \( 3x + 9 = \frac{5x}{3} \)
   \( 3(3x+9) = 5x \)
   \( 9x + 27 = 5x \)
   \( 27 = 5x - 9x \)
   \( 27 = -4x \)
   \( x = -\frac{27}{4} \)
3. \( \frac{9x+6}{7} + 3 = \frac{7x}{6} \)
   \( \frac{9x+6+21}{7} = \frac{7x}{6} \)
   \( \frac{9x+27}{7} = \frac{7x}{6} \)
   \( 6(9x+27) = 7(7x) \)
   \( 54x + 162 = 49x \)
   \( 162 = 49x - 54x \)
   \( 162 = -5x \)
   \( x = -\frac{162}{5} \)

Ответ: 1) 2; 2) -27/4; 3) -162/5.