4. Упростите выражение 6 3/4 x - x + 3 5/12 x и найдите его значение при x=1 7/11.

$$6 \frac{3}{4} x - x + 3 \frac{5}{12} x = (6 \frac{3}{4} - 1 + 3 \frac{5}{12}) x$$.

$$6 \frac{3}{4} - 1 + 3 \frac{5}{12} = 6 + \frac{3}{4} - 1 + 3 + \frac{5}{12} = 6 - 1 + 3 + \frac{3}{4} + \frac{5}{12} = 8 + \frac{3 \cdot 3}{4 \cdot 3} + \frac{5}{12} = 8 + \frac{9}{12} + \frac{5}{12} = 8 + \frac{14}{12} = 8 + \frac{7}{6} = 8 + 1 \frac{1}{6} = 9 \frac{1}{6}$$.

$$x = 1 \frac{7}{11} = \frac{1 \cdot 11 + 7}{11} = \frac{11 + 7}{11} = \frac{18}{11}$$.

$$9 \frac{1}{6} \cdot \frac{18}{11} = \frac{9 \cdot 6 + 1}{6} \cdot \frac{18}{11} = \frac{54 + 1}{6} \cdot \frac{18}{11} = \frac{55}{6} \cdot \frac{18}{11} = \frac{55 \cdot 18}{6 \cdot 11} = \frac{5 \cdot 11 \cdot 3 \cdot 6}{6 \cdot 11} = 5 \cdot 3 = 15$$.

Ответ: $$15$$