201. Найдите корень уравнения: 1) 3(x-2) = x+2 2; 2) 5-2(x-1) = 4-x; 3) (7x+1)-(9x + 3) = 5; 4) 3,4 + 2y = 7(y – 2,3); 5) 0,2(7-2y) = 2,3 – 0,3(y – 6); 6) 2/3(1/3x-1/2)=4x+21/2.

Решение:

1. \( 3(x-2) = x+2 \)
   \( 3x - 6 = x + 2 \)
   \( 3x - x = 2 + 6 \)
   \( 2x = 8 \)
   \( x = \frac{8}{2} \)
   \( x = 4 \)
2. \( 5 - 2(x-1) = 4 - x \)
   \( 5 - 2x + 2 = 4 - x \)
   \( 7 - 2x = 4 - x \)
   \( 7 - 4 = -x + 2x \)
   \( 3 = x \)
3. \( (7x+1) - (9x + 3) = 5 \)
   \( 7x + 1 - 9x - 3 = 5 \)
   \( -2x - 2 = 5 \)
   \( -2x = 5 + 2 \)
   \( -2x = 7 \)
   \( x = -\frac{7}{2} \)
   \( x = -3,5 \)
4. \( 3,4 + 2y = 7(y - 2,3) \)
   \( 3,4 + 2y = 7y - 16,1 \)
   \( 3,4 + 16,1 = 7y - 2y \)
   \( 19,5 = 5y \)
   \( y = \frac{19,5}{5} \)
   \( y = 3,9 \)
5. \( 0,2(7-2y) = 2,3 - 0,3(y - 6) \)
   \( 1,4 - 0,4y = 2,3 - 0,3y + 1,8 \)
   \( 1,4 - 0,4y = 4,1 - 0,3y \)
   \( 1,4 - 4,1 = -0,3y + 0,4y \)
   \( -2,7 = 0,1y \)
   \( y = \frac{-2,7}{0,1} \)
   \( y = -27 \)
6. \( \frac{2}{3}(\frac{1}{3}x - \frac{1}{2}) = 4x + 2\frac{1}{2} \)
   \( \frac{2}{9}x - \frac{1}{3} = 4x + \frac{5}{2} \)
   \( \frac{2}{9}x - 4x = \frac{5}{2} + \frac{1}{3} \)
   \( (\frac{2}{9} - \frac{36}{9})x = \frac{15}{6} + \frac{2}{6} \)
   \( -\frac{34}{9}x = \frac{17}{6} \)
   \( x = \frac{17}{6} \cdot (-\frac{9}{34}) \)
   \( x = \frac{1}{6} \cdot (-\frac{9}{2}) \)
   \( x = -\frac{9}{12} \)
   \( x = -\frac{3}{4} \)

Ответ: 1) 4; 2) 3; 3) -3,5; 4) 3,9; 5) -27; 6) -3/4.