201. Найдите корень уравнения:

Решение:

1. \( 4(x - 3) = x + 6 \)

\( 4x - 12 = x + 6 \)
\( 4x - x = 6 + 12 \)
\( 3x = 18 \)
\( x = \frac{18}{3} \)
\( x = 6 \)

2. \( 4 - 6(x + 2) = 3 - 5x \)

\( 4 - 6x - 12 = 3 - 5x \)
\( -8 - 6x = 3 - 5x \)
\( -8 - 3 = -5x + 6x \)
\( -11 = x \)
\( x = -11 \)

3. \( (5x + 8) - (8x + 14) = 9 \)

\( 5x + 8 - 8x - 14 = 9 \)
\( -3x - 6 = 9 \)
\( -3x = 9 + 6 \)
\( -3x = 15 \)
\( x = \frac{15}{-3} \)
\( x = -5 \)

4. \( 2,7 + 3y = 9(y - 2,1) \)

\( 2,7 + 3y = 9y - 18,9 \)
\( 2,7 + 18,9 = 9y - 3y \)
\( 21,6 = 6y \)
\( y = \frac{21,6}{6} \)
\( y = 3,6 \)

5. \( 0,3(8 – 3y) = 3,2 – 0,8(y – 7) \)

\( 2,4 - 0,9y = 3,2 - 0,8y + 5,6 \)
\( 2,4 - 0,9y = 8,8 - 0,8y \)
\( -0,9y + 0,8y = 8,8 - 2,4 \)
\( -0,1y = 6,4 \)
\( y = \frac{6,4}{-0,1} \)
\( y = -64 \)

6. \( \frac{5}{6}(\frac{1}{3}x - \frac{1}{5}) = 3x + 3\frac{1}{3} \)

\( \frac{5}{18}x - \frac{5}{30} = 3x + \frac{10}{3} \)
\( \frac{5}{18}x - \frac{1}{6} = 3x + \frac{10}{3} \)
\( \frac{5}{18}x - 3x = \frac{10}{3} + \frac{1}{6} \)
\( \frac{5 - 54}{18}x = \frac{20 + 1}{6} \)
\( -\frac{49}{18}x = \frac{21}{6} \)
\( -\frac{49}{18}x = \frac{7}{2} \)
\( x = \frac{7}{2} \cdot \frac{-18}{49} \)
\( x = \frac{1}{1} \cdot \frac{-9}{7} \)
\( x = -\frac{9}{7} \)

Ответ: 1) 6; 2) -11; 3) -5; 4) 3,6; 5) -64; 6) -9/7.