262. При каком значении х равны значения выражений: 1) 1/2(x - 7) + 1 и 3(1-x)/4 2) 2/5(3-2x) и 3(1+3x)/10 - 4/5 3) 1/3(x + 2) и 2x-1/3 4) 2-3x/4 и 3(x+1)/8 - 1?

Решение:

1. \( \frac{1}{2}(x - 7) + 1 = \frac{3(1-x)}{4} \)
   \( \frac{x-7}{2} + 1 = \frac{3-3x}{4} \)
   \( 2(x-7) + 4 = 3(1-x) \)
   \( 2x - 14 + 4 = 3 - 3x \)
   \( 2x - 10 = 3 - 3x \)
   \( 2x + 3x = 3 + 10 \)
   \( 5x = 13 \)
   \( x = \frac{13}{5} \)
2. \( \frac{2}{5}(3-2x) = \frac{3(1+3x)}{10} - \frac{4}{5} \)
   \( \frac{6-4x}{5} = \frac{3+9x}{10} - \frac{8}{10} \)
   \( 2(6-4x) = 3+9x - 8 \)
   \( 12 - 8x = 9x - 5 \)
   \( 12 + 5 = 9x + 8x \)
   \( 17 = 17x \)
   \( x = 1 \)
3. \( \frac{1}{3}(x + 2) = \frac{2x-1}{3} \)
   \( x + 2 = 2x - 1 \)
   \( 2 + 1 = 2x - x \)
   \( 3 = x \)
4. \( \frac{2-3x}{4} = \frac{3(x+1)}{8} - 1 \)
   \( 2(2-3x) = 3(x+1) - 8 \)
   \( 4 - 6x = 3x + 3 - 8 \)
   \( 4 - 6x = 3x - 5 \)
   \( 4 + 5 = 3x + 6x \)
   \( 9 = 9x \)
   \( x = 1 \)

Ответ: 1) \( x = \frac{13}{5} \); 2) \( x = 1 \); 3) \( x = 3 \); 4) \( x = 1 \).