10. Решите уравнение: 1) 4x = 24 + x; 2) 8x − 8 = 20 – 6x; 3) 9 - 4x = 3x – 40; 4) 0,6x – 5,4 = -0,8x + 5,8; 5) 4,7 – 1,1x = 0,5x – 3,3; 6) S/6 x + 16 = S/4 x + 9.

Решение:

1. \( 4x = 24 + x \)
   \( 4x - x = 24 \)
   \( 3x = 24 \)
   \( x = \frac{24}{3} \)
   \( x = 8 \)


2. \( 8x - 8 = 20 - 6x \)
   \( 8x + 6x = 20 + 8 \)
   \( 14x = 28 \)
   \( x = \frac{28}{14} \)
   \( x = 2 \)


3. \( 9 - 4x = 3x - 40 \)
   \( 9 + 40 = 3x + 4x \)
   \( 49 = 7x \)
   \( x = \frac{49}{7} \)
   \( x = 7 \)


4. \( 0,6x - 5,4 = -0,8x + 5,8 \)
   \( 0,6x + 0,8x = 5,8 + 5,4 \)
   \( 1,4x = 11,2 \)
   \( x = \frac{11,2}{1,4} \)
   \( x = 8 \)


5. \( 4,7 - 1,1x = 0,5x - 3,3 \)
   \( 4,7 + 3,3 = 0,5x + 1,1x \)
   \( 8 = 1,6x \)
   \( x = \frac{8}{1,6} \)
   \( x = 5 \)


6. \( \frac{5}{6} x + 16 = \frac{4}{9} x + 9 \)
   \( \frac{5}{6} x - \frac{4}{9} x = 9 - 16 \)
   \( \frac{15}{18} x - \frac{8}{18} x = -7 \)
   \( \frac{7}{18} x = -7 \)
   \( x = -7 \cdot \frac{18}{7} \)
   \( x = -18 \)

Ответ: 1) x = 8; 2) x = 2; 3) x = 7; 4) x = 8; 5) x = 5; 6) x = -18.