142. Решите уравнение: a) \(\frac{5}{9} x = 1\) б) \(\frac{2}{14} x = 1\) в) \(m + \frac{3}{10} m = 1\) г) \(z - \frac{2}{15} z = 1\)

Решение:

• а) \(\frac{5}{9} x = 1\)
• \(x = 1 : \frac{5}{9} = 1 \times \frac{9}{5} = \frac{9}{5}\)
• б) \(\frac{2}{14} x = 1\)
• \(\frac{1}{7} x = 1\)
• \(x = 1 : \frac{1}{7} = 1 \times 7 = 7\)
• в) \(m + \frac{3}{10} m = 1\)
• \(1m + \frac{3}{10} m = 1\)
• \(\left(1 + \frac{3}{10}\right) m = 1\)
• \(\frac{13}{10} m = 1\)
• \(m = 1 : \frac{13}{10} = 1 \times \frac{10}{13} = \frac{10}{13}\)
• г) \(z - \frac{2}{15} z = 1\)
• \(1z - \frac{2}{15} z = 1\)
• \(\left(1 - \frac{2}{15}\right) z = 1\)
• \(\frac{13}{15} z = 1\)
• \(z = 1 : \frac{13}{15} = 1 \times \frac{15}{13} = \frac{15}{13}\)

Ответ:

• а) \(x = \frac{9}{5}\)
• б) \(x = 7\)
• в) \(m = \frac{10}{13}\)
• г) \(z = \frac{15}{13}\)