№3. Решите уравнения: 1)x+3/4=11/12; 2)x-14/15=1/6 3)30/41-x=5/82

Решение:

1) \[ x + \frac{3}{4} = \frac{11}{12}\]

\[x = \frac{11}{12} - \frac{3}{4}\]

\[x = \frac{11}{12} - \frac{3 \cdot 3}{4 \cdot 3}\]

\[x = \frac{11}{12} - \frac{9}{12}\]

\[x = \frac{11 - 9}{12}\]

\[x = \frac{2}{12}\]

\[x = \frac{1}{6}\]

2) \[ x - \frac{14}{15} = \frac{1}{6}\]

\[x = \frac{1}{6} + \frac{14}{15}\]

\[x = \frac{1 \cdot 5}{6 \cdot 5} + \frac{14 \cdot 2}{15 \cdot 2}\]

\[x = \frac{5}{30} + \frac{28}{30}\]

\[x = \frac{5 + 28}{30}\]

\[x = \frac{33}{30}\]

\[x = \frac{11}{10} = 1 \frac{1}{10}\]

3) \[ \frac{30}{41} - x = \frac{5}{82}\]

\[x = \frac{30}{41} - \frac{5}{82}\]

\[x = \frac{30 \cdot 2}{41 \cdot 2} - \frac{5}{82}\]

\[x = \frac{60}{82} - \frac{5}{82}\]

\[x = \frac{60 - 5}{82}\]

\[x = \frac{55}{82}\]