200. Решите уравнение:

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. \( 0,6x - 5,4 = -0,8x + 5,8 \)

\( 0,6x + 0,8x = 5,8 + 5,4 \)
\( 1,4x = 11,2 \)
\( x = \frac{11,2}{1,4} = \frac{112}{14} \)
\( x = 8 \)

5. \( 4,7 - 1,1x = 0,5x - 3,3 \)

\( 4,7 + 3,3 = 0,5x + 1,1x \)
\( 8 = 1,6x \)
\( x = \frac{8}{1,6} = \frac{80}{16} \)
\( x = 5 \)

6. \( \frac{5}{6}x + 16 = \frac{4}{9}x + 9 \)

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

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