201. Найдите корень уравнения: 1) 5(x - 4) = x + 8; 2) 9 - 7(x + 3) = 5 - 6x; 3) (7x + 9) - (11x - 7) = 8; 4) 19,6 + y = 7(1,2 – y); 5) 0,4(6 - 4y) = 0,5(7 – 3y) – 1,9; 6) 3/4 (1/6 x - 1/3) = 2x - 11 1/2.

Ответ: 1) x = 7, 2) x = -17, 3) x = 2, 4) y = -3,08, 5) y = 12, 6) x = 6

Решение:

1) 5(x - 4) = x + 8

5x - 20 = x + 8

5x - x = 8 + 20

4x = 28

x = 28 : 4

x = 7

2) 9 - 7(x + 3) = 5 - 6x

9 - 7x - 21 = 5 - 6x

-7x + 6x = 5 - 9 + 21

-x = 17

x = -17

3) (7x + 9) - (11x - 7) = 8

7x + 9 - 11x + 7 = 8

7x - 11x = 8 - 9 - 7

-4x = -8

x = -8 : (-4)

x = 2

4) 19,6 + y = 7(1,2 – y)

19,6 + y = 8,4 - 7y

y + 7y = 8,4 - 19,6

8y = -11,2

y = -11,2 : 8

y = -1,4

5) 0,4(6 - 4y) = 0,5(7 – 3y) – 1,9

2,4 - 1,6y = 3,5 - 1,5y - 1,9

-1,6y + 1,5y = 3,5 - 1,9 - 2,4

-0,1y = -0,8

y = -0,8 : (-0,1)

y = 8

6) \(\frac{3}{4}(\frac{1}{6}x - \frac{1}{3}) = 2x - 11 \frac{1}{2}\)

\(\frac{3}{4} \cdot \frac{1}{6}x - \frac{3}{4} \cdot \frac{1}{3} = 2x - \frac{11 \cdot 2 + 1}{2}\)

\(\frac{3}{24}x - \frac{3}{12} = 2x - \frac{23}{2}\)

\(\frac{1}{8}x - \frac{1}{4} = 2x - \frac{23}{2}\)

\(\frac{1}{8}x - 2x = \frac{1}{4} - \frac{23}{2}\)

\(\frac{1}{8}x - \frac{2 \cdot 8}{8}x = \frac{1}{4} - \frac{23 \cdot 2}{2 \cdot 2}\)

\(\frac{1}{8}x - \frac{16}{8}x = \frac{1}{4} - \frac{46}{4}\)

\(-\frac{15}{8}x = -\frac{45}{4}\)

\(x = -\frac{45}{4} : (-\frac{15}{8})\)

\(x = \frac{45}{4} \cdot \frac{8}{15}\)

\(x = \frac{3 \cdot 2}{1} = 6\)

Ответ: 1) x = 7, 2) x = -17, 3) x = 2, 4) y = -3,08, 5) y = 12, 6) x = 6