Решите уравнение: 1) 1/3 x + 1/4 x + 1/8 x = 34/45; 2) 3 3/4 x - 1 2/3 x = 2 11/12; 3) 4 2/15 - 3 1/9 x = 1 4/5; 4) 4/15 x + 2 1/3 = 7 8/15.

Решение:

1. Решение уравнения:

\(\frac{1}{3}x + \frac{1}{4}x + \frac{1}{8}x = \frac{34}{45}\)

\(x \left( \frac{1}{3} + \frac{1}{4} + \frac{1}{8} \right) = \frac{34}{45}\)

\(x \left( \frac{8 + 6 + 3}{24} \right) = \frac{34}{45}\)

\(x \cdot \frac{17}{24} = \frac{34}{45}\)

\(x = \frac{34}{45} \cdot \frac{24}{17} = \frac{2 \cdot 24}{45} = \frac{48}{45} = \frac{16}{15}\)

2. Решение уравнения:

\(3 \frac{3}{4}x - 1 \frac{2}{3}x = 2 \frac{11}{12}\)

\(x \left( \frac{15}{4} - \frac{5}{3} \right) = \frac{35}{12}\)

\(x \left( \frac{45 - 20}{12} \right) = \frac{35}{12}\)

\(x \cdot \frac{25}{12} = \frac{35}{12}\)

\(x = \frac{35}{12} \cdot \frac{12}{25} = \frac{35}{25} = \frac{7}{5}\)

3. Решение уравнения:

\(4 \frac{2}{15} - 3 \frac{1}{9}x = 1 \frac{4}{5}\)

\(\frac{62}{15} - \frac{28}{9}x = \frac{9}{5}\)

\(\frac{28}{9}x = \frac{62}{15} - \frac{9}{5}\)

\(\frac{28}{9}x = \frac{62 - 27}{15} = \frac{35}{15} = \frac{7}{3}\)

\(x = \frac{7}{3} \cdot \frac{9}{28} = \frac{1 \cdot 3}{1 \cdot 4} = \frac{3}{4}\)

4. Решение уравнения:

\(\frac{4}{15}x + 2 \frac{1}{3} = 7 \frac{8}{15}\)

\(\frac{4}{15}x = 7 \frac{8}{15} - 2 \frac{1}{3}\)

\(\frac{4}{15}x = \frac{113}{15} - \frac{7}{3}\)

\(\frac{4}{15}x = \frac{113 - 35}{15} = \frac{78}{15}\)

\(x = \frac{78}{15} \cdot \frac{15}{4} = \frac{78}{4} = \frac{39}{2}\)

Ответ: 1) x = 16/15; 2) x = 7/5; 3) x = 3/4; 4) x = 39/2.