3. Решить уравнение 3 5 8 5 a) 8--x = 3-6) (x-9)+5=6 4 16 21 14

Ответ: Решение уравнения

a) \(8 \frac{3}{4} - x = 3 \frac{5}{16}\)\[8 \frac{3}{4} - 3 \frac{5}{16} = x\]\[x = 8 + \frac{3}{4} - 3 - \frac{5}{16}\]\[x = 5 + \frac{3}{4} - \frac{5}{16}\]Общий знаменатель 16.\[\frac{3}{4} = \frac{3 \cdot 4}{4 \cdot 4} = \frac{12}{16}\]\[x = 5 + \frac{12}{16} - \frac{5}{16}\]\[x = 5 + \frac{7}{16}\]\[x = 5 \frac{7}{16}\]

б) \((x - 9) \frac{3}{7} + 5 \frac{8}{21} = 6 \frac{5}{14}\)\[(x - 9) \frac{3}{7} = 6 \frac{5}{14} - 5 \frac{8}{21}\]\[(x - 9) \frac{3}{7} = 6 + \frac{5}{14} - 5 - \frac{8}{21}\]\[(x - 9) \frac{3}{7} = 1 + \frac{5}{14} - \frac{8}{21}\]Общий знаменатель 42.\[\frac{5}{14} = \frac{5 \cdot 3}{14 \cdot 3} = \frac{15}{42}\]\[\frac{8}{21} = \frac{8 \cdot 2}{21 \cdot 2} = \frac{16}{42}\]\[(x - 9) \frac{3}{7} = 1 + \frac{15}{42} - \frac{16}{42}\]\[(x - 9) \frac{3}{7} = 1 - \frac{1}{42}\]\[(x - 9) \frac{3}{7} = \frac{41}{42}\]\[x - 9 = \frac{41}{42} : \frac{3}{7}\]\[x - 9 = \frac{41}{42} \cdot \frac{7}{3}\]\[x - 9 = \frac{41 \cdot 1}{6 \cdot 3}\]\[x - 9 = \frac{41}{18}\]\[x = \frac{41}{18} + 9\]\[x = \frac{41}{18} + \frac{9 \cdot 18}{18}\]\[x = \frac{41}{18} + \frac{162}{18}\]\[x = \frac{203}{18}\]\[x = 11 \frac{5}{18}\]

Ответ: Уравнения решены.