Решите уравнения: 1) \(|x + \frac{5}{12}| - 1\frac{1}{6} = 1\frac{1}{4}\) 2) \(|x - 0.25| + 3\frac{1}{2} = 4\frac{1}{3}\)

Решение:

1. Уравнение 1: \(
   \)|x + \(\frac{5}{12}\)| - 1\(\frac{1}{6}\) = 1\(\frac{1}{4}\)
   \)|x + \(\frac{5}{12}\)| = 1\(\frac{1}{4}\) + 1\(\frac{1}{6}\)
   \)|x + \(\frac{5}{12}\)| = \(\frac{5}{4}\) + \(\frac{7}{6}\)
   \)|x + \(\frac{5}{12}\)| = \(\frac{15}{12}\) + \(\frac{14}{12}\)
   \)|x + \(\frac{5}{12}\)| = \(\frac{29}{12}\)
   
   Раскрываем модуль:
   
   Случай 1: \(x + \frac{5}{12} = \frac{29}{12}\)
   \(x = \frac{29}{12} - \frac{5}{12}\)
   \(x = \frac{24}{12}\)
   \(x = 2\)
   
   Случай 2: \(x + \frac{5}{12} = -\frac{29}{12}\)
   \(x = -\frac{29}{12} - \frac{5}{12}\)
   \(x = -\frac{34}{12}\)
   \(x = -\frac{17}{6}\)
   
2. Уравнение 2: \(
   \)|x - 0.25| + 3\(\frac{1}{2}\) = 4\(\frac{1}{3}\)\)
   \)|x - 0.25| = 4\(\frac{1}{3}\) - 3\(\frac{1}{2}\)\)
   \)|x - \(\frac{1}{4}\)| = \(\frac{13}{3}\) - \(\frac{7}{2}\)\)
   \)|x - \(\frac{1}{4}\)| = \(\frac{26}{6}\) - \(\frac{21}{6}\)\)
   \)|x - \(\frac{1}{4}\)| = \(\frac{5}{6}\)\)
   
   Раскрываем модуль:
   
   Случай 1: \(x - \frac{1}{4} = \frac{5}{6}\)
   \(x = \frac{5}{6} + \frac{1}{4}\)
   \(x = \frac{10}{12} + \frac{3}{12}\)
   \(x = \frac{13}{12}\)
   
   Случай 2: \(x - \frac{1}{4} = -\frac{5}{6}\)
   \(x = -\frac{5}{6} + \frac{1}{4}\)
   \(x = -\frac{10}{12} + \frac{3}{12}\)
   \(x = -\frac{7}{12}\)
   

Ответ: 1) x = 2; x = -\(\frac{17}{6}\); 2) x = \(\frac{13}{12}\); x = -\(\frac{7}{12}\).