7. Решите уравнение: a) \(3 \frac{2}{15} x + 1 \frac{7}{10} x = 9 \frac{2}{3}\) б) \(5,4 x - 2,6 x = 10,84 – 2,3\)

Решение:

a) \(3 \frac{2}{15} x + 1 \frac{7}{10} x = 9 \frac{2}{3}\)

\((\frac{3 \cdot 15 + 2}{15}) x + (\frac{1 \cdot 10 + 7}{10}) x = \frac{9 \cdot 3 + 2}{3}\)

\((\frac{47}{15}) x + (\frac{17}{10}) x = \frac{29}{3}\)

\((\frac{47 \cdot 2}{15 \cdot 2}) x + (\frac{17 \cdot 3}{10 \cdot 3}) x = \frac{29}{3}\)

\((\frac{94}{30}) x + (\frac{51}{30}) x = \frac{29}{3}\)

\(\frac{145}{30} x = \frac{29}{3}\)

\(x = \frac{29}{3} : \frac{145}{30}\)

\(x = \frac{29}{3} \cdot \frac{30}{145}\)

\(x = \frac{29 \cdot 30}{3 \cdot 145}\)

\(x = \frac{1 \cdot 10}{1 \cdot 5}\)

\(x = \frac{10}{5} = 2\)

б) \(5,4 x - 2,6 x = 10,84 - 2,3\)

\(2,8 x = 8,54\)

\(x = \frac{8,54}{2,8} = 3,05\)

Ответ: a) 2; б) 3,05