201. Найдите корень уравнения: 1) 3(x - 2) = x + 2; 2) 5 - 2(x - 1) = 4 - x; 3) (7x + 1)(9x + 3) = 5; 4) 3,4(2y - 2,3) = 7(y - 2,3); 5) 0,2(7y) = 2,3 - 0,3(y - 6).

Решение:

1. 1) \( 3(x - 2) = x + 2 \)
   \( 3x - 6 = x + 2 \)
   \( 3x - x = 2 + 6 \)
   \( 2x = 8 \)
   \( x = 4 \)
2. 2) \( 5 - 2(x - 1) = 4 - x \)
   \( 5 - 2x + 2 = 4 - x \)
   \( 7 - 2x = 4 - x \)
   \( 7 - 4 = 2x - x \)
   \( 3 = x \)
3. 3) \( (7x + 1)(9x + 3) = 5 \)
   \( 63x^2 + 21x + 9x + 3 = 5 \)
   \( 63x^2 + 30x - 2 = 0 \)
   \( D = 30^2 - 4 \cdot 63 \cdot (-2) = 900 + 504 = 1404 \)
   \( \sqrt{D} = \sqrt{1404} \approx 37.47 \)
   \( x_{1,2} = \frac{-30 \pm \sqrt{1404}}{2 \cdot 63} = \frac{-30 \pm 37.47}{126} \)
   \( x_1 = \frac{7.47}{126} \approx 0.059 \)
   \( x_2 = \frac{-67.47}{126} \approx -0.535 \)
4. 4) \( 3,4(2y - 2,3) = 7(y - 2,3) \)
   \( 6,8y - 7,82 = 7y - 16,1 \)
   \( 16,1 - 7,82 = 7y - 6,8y \)
   \( 8,28 = 0,2y \)
   \( y = \frac{8,28}{0,2} = 41,4 \)
5. 5) \( 0,2(7y) = 2,3 - 0,3(y - 6) \)
   \( 1,4y = 2,3 - 0,3y + 1,8 \)
   \( 1,4y = 4,1 - 0,3y \)
   \( 1,4y + 0,3y = 4,1 \)
   \( 1,7y = 4,1 \)
   \( y = \frac{4,1}{1,7} = \frac{41}{17} \)

Ответ: 1) 4; 2) 3; 3) ≈ 0.059; -0.535; 4) 41,4; 5) 41/17.