Найдите корень уравнения: 5.122. а) -30(x - 21) = -180; б) (15 - 9x)4 = 204; в) 9/4 x - 5/14 = 1/7; г) (3,6 - 0,2x)4,9 = 9,8; д) (7х - 3,4)9 = 13,5; е) 1/3 x + 5/6 x = 3,5.

Решение:

1. а)
   • \[ -30(x - 21) = -180 \]
   • \[ x - 21 = \frac{-180}{-30} \]
   • \[ x - 21 = 6 \]
   • \[ x = 6 + 21 \]
   • \[ x = 27 \]
2. б)
   • \[ (15 - 9x)4 = 204 \]
   • \[ 15 - 9x = \frac{204}{4} \]
   • \[ 15 - 9x = 51 \]
   • \[ -9x = 51 - 15 \]
   • \[ -9x = 36 \]
   • \[ x = \frac{36}{-9} \]
   • \[ x = -4 \]
3. в)
   • \[ \frac{9}{4}x - \frac{5}{14} = \frac{1}{7} \]
   • \[ \frac{9}{4}x = \frac{1}{7} + \frac{5}{14} \]
   • \[ \frac{9}{4}x = \frac{2}{14} + \frac{5}{14} \]
   • \[ \frac{9}{4}x = \frac{7}{14} \]
   • \[ \frac{9}{4}x = \frac{1}{2} \]
   • \[ x = \frac{1}{2} \times \frac{4}{9} \]
   • \[ x = \frac{4}{18} \]
   • \[ x = \frac{2}{9} \]
4. г)
   • \[ (3,6 - 0,2x)4,9 = 9,8 \]
   • \[ 3,6 - 0,2x = \frac{9,8}{4,9} \]
   • \[ 3,6 - 0,2x = 2 \]
   • \[ -0,2x = 2 - 3,6 \]
   • \[ -0,2x = -1,6 \]
   • \[ x = \frac{-1,6}{-0,2} \]
   • \[ x = 8 \]
5. д)
   • \[ (7x - 3,4)9 = 13,5 \]
   • \[ 7x - 3,4 = \frac{13,5}{9} \]
   • \[ 7x - 3,4 = 1,5 \]
   • \[ 7x = 1,5 + 3,4 \]
   • \[ 7x = 4,9 \]
   • \[ x = \frac{4,9}{7} \]
   • \[ x = 0,7 \]
6. е)
   • \[ \frac{1}{3}x + \frac{5}{6}x = 3,5 \]
   • \[ \frac{2}{6}x + \frac{5}{6}x = 3,5 \]
   • \[ \frac{7}{6}x = 3,5 \]
   • \[ x = 3,5 \times \frac{6}{7} \]
   • \[ x = \frac{35}{10} \times \frac{6}{7} \]
   • \[ x = \frac{7}{2} \times \frac{6}{7} \]
   • \[ x = \frac{6}{2} \]
   • \[ x = 3 \]

Ответ: а) 27; б) -4; в) 2/9; г) 8; д) 0,7; е) 3.