Решите уравнение: 1) 3(x - 2) = x + 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) \(\frac{1}{2}\)\(\frac{1}{3}x - \frac{1}{2}\) = 4x + \(\frac{21}{2}\).

Решение:

1. \( 3(x - 2) = x + 2 \)
1. \( 3x - 6 = x + 2 \)
2. \( 3x - x = 2 + 6 \)
3. \( 2x = 8 \)
4. \( x = 4 \)
2. \( 5 - 2(x - 1) = 4 - x \)
1. \( 5 - 2x + 2 = 4 - x \)
2. \( 7 - 2x = 4 - x \)
3. \( 7 - 4 = 2x - x \)
4. \( 3 = x \)
5. \( x = 3 \)
3. \( (7x + 1) - (9x + 3) = 5 \)
1. \( 7x + 1 - 9x - 3 = 5 \)
2. \( -2x - 2 = 5 \)
3. \( -2x = 5 + 2 \)
4. \( -2x = 7 \)
5. \( x = -\frac{7}{2} \)
6. \( x = -3,5 \)
4. \( 3,4 + 2y = 7(y - 2,3) \)
1. \( 3,4 + 2y = 7y - 16,1 \)
2. \( 3,4 + 16,1 = 7y - 2y \)
3. \( 19,5 = 5y \)
4. \( y = \frac{19,5}{5} \)
5. \( y = 3,9 \)
5. \( 0,2(7-2y) = 2,3 - 0,3(y - 6) \)
1. \( 1,4 - 0,4y = 2,3 - 0,3y + 1,8 \)
2. \( 1,4 - 0,4y = 4,1 - 0,3y \)
3. \( 1,4 - 4,1 = 0,4y - 0,3y \)
4. \( -2,7 = 0,1y \)
5. \( y = \frac{-2,7}{0,1} \)
6. \( y = -27 \)
6. \( \frac{1}{2}( \frac{1}{3}x - \frac{1}{2} ) = 4x + \frac{21}{2} \)
1. \( \frac{1}{6}x - \frac{1}{4} = 4x + \frac{21}{2} \)
2. \( \frac{1}{6}x - 4x = \frac{21}{2} + \frac{1}{4} \)
3. \( \frac{x - 24x}{6} = \frac{42 + 1}{4} \)
4. \( \frac{-23x}{6} = \frac{43}{4} \)
5. \( -23x \cdot 4 = 43 \cdot 6 \)
6. \( -92x = 258 \)
7. \( x = \frac{258}{-92} \)
8. \( x = -\frac{129}{46} \)

Ответ: 1) x = 4; 2) x = 3; 3) x = -3,5; 4) y = 3,9; 5) y = -27; 6) x = -⅝⅞.