Решите уравнение: a) -2x+16= 5x + 30; б) 3\frac{1}{4}x-4\frac{5}{7}=3\frac{5}{12}x-3\frac{3}{14}; в) \frac{5}{12}-\frac{7}{9}x=10-\frac{5}{12}-3x.

Решение:

1. Уравнение а:
   
   • -2x + 16 = 5x + 30
   • -2x - 5x = 30 - 16
   • -7x = 14
   • x = \frac{14}{-7}
   • x = -2
2. Уравнение б:
   
   • \(3\frac{1}{4}x - 4\frac{5}{7} = 3\frac{5}{12}x - 3\frac{3}{14}\)
   • \(\frac{13}{4}x - \frac{33}{7} = \frac{41}{12}x - \frac{45}{14}\)
   • \(\frac{13}{4}x - \frac{41}{12}x = \frac{33}{7} - \frac{45}{14}\)
   • \(\frac{39}{12}x - \frac{41}{12}x = \frac{66}{14} - \frac{45}{14}\)
   • \(-\frac{2}{12}x = \frac{21}{14}\)
   • \(-\frac{1}{6}x = \frac{3}{2}\)
   • x = \frac{3}{2} \times (-6)
   • x = -9
3. Уравнение в:
   
   • \(\frac{5}{12} - \frac{7}{9}x = 10 - \frac{5}{12} - 3x\)
   • \(\frac{5}{12} + \frac{5}{12} - 10 = \frac{7}{9}x - 3x\)
   • \(\frac{10}{12} - 10 = \frac{7}{9}x - \frac{27}{9}x\)
   • \(\frac{5}{6} - \frac{60}{6} = \frac{7-27}{9}x\)
   • \(-\frac{55}{6} = -\frac{20}{9}x\)
   • x = \frac{-55}{6} \times \frac{9}{-20}\)
   • x = \frac{55}{6} \times \frac{9}{20}\)
   • x = \frac{11}{2} \times \frac{3}{4}\)
   • x = \frac{33}{8}\)

Ответ: а) x = -2; б) x = -9; в) x = \frac{33}{8}