Решите уравнение:
1)

\frac{x - 7}{4} - \frac{x}{6} = 2

;
2)

\frac{x + 6}{2} - \frac{x - 7}{7} = 4

;
3)

\frac{2 x + 3}{6} + \frac{1 - 4 x}{8} = \frac{1}{3}

;
4)

3 x - \frac{2 x + 3}{2} = \frac{x + 6}{3}

;
5)

\frac{6 x - 7}{5} - \frac{3 x + 1}{6} = \frac{11 - x}{15}

;
6)

\frac{5 x - 3}{9} - \frac{4 x + 3}{6} = x - 1

;
7)

\frac{8 x - 5}{3} - \frac{4 x + 3}{4} + \frac{2 - 9 x}{2} = - 3

;
8)

\frac{8 x^{2} - 3 x}{16} - \frac{6 x^{2} + 1}{12} = - 1

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Алгебре 7 класс Мерзляк. Номер №375

\frac{x - 7}{4} - \frac{x}{6} = 2

\frac{3 (x - 7) - 2 x}{12} = 2

3(x − 7) − 2x = 2 * 12
3x − 21 − 2x = 24
3x − 2x = 24 + 21
x = 45

\frac{x + 6}{2} - \frac{x - 7}{7} = 4

\frac{7 (x + 6) - 2 (x - 7)}{14} = 4

7(x + 6) − 2(x − 7) = 4 * 14
7x + 42 − 2x + 14 = 56
7x − 2x = 56 − 42 − 14
5x = 0
x = 0

\frac{2 x + 3}{6} + \frac{1 - 4 x}{8} = \frac{1}{3}

\frac{4 (2 x + 3) + 3 (1 - 4 x)}{24} = \frac{1}{3}

4 (2 x + 3) + 3 (1 - 4 x) = \frac{1}{3} * 24

8x + 12 + 3 − 12x = 8
8x − 12x = 8 − 12 − 3
−4x = −7

x = \frac{7}{4} = 1 \frac{3}{4}

x = 1,25

3 x - \frac{2 x + 3}{2} = \frac{x + 6}{3}

3 x - \frac{2 x + 3}{2} - \frac{x + 6}{3} = 0

\frac{6 * 3 x - 3 (2 x + 3) - 2 (x + 6)}{6} = 0

6 * 3x − 3(2x + 3) − 2(x + 6) = 0
18x − 6x − 9 − 2x − 12 = 0
18x − 6x − 2x = 9 + 12
10x = 21
x = 21 : 10
x = 2,1

\frac{6 x - 7}{5} - \frac{3 x + 1}{6} = \frac{11 - x}{15}

\frac{6 x - 7}{5} - \frac{3 x + 1}{6} - \frac{11 - x}{15} = 0

\frac{6 (6 x - 7) - 5 (3 x + 1) - 2 (11 - x)}{30} = 0

6(6x − 7) − 5(3x + 1) − 2(11 − x) = 0
36x − 42 − 15x − 5 − 22 + 2x = 0
36x − 15x + 2x = 42 + 5 + 22
23x = 69
x = 69 : 23
x = 3

\frac{5 x - 3}{9} - \frac{4 x + 3}{6} = x - 1

\frac{5 x - 3}{9} - \frac{4 x + 3}{6} - x = - 1

\frac{2 (5 x - 3) - 3 (4 x + 3) - 18 x}{18} = - 1

2(5x − 3) − 3(4x + 3) − 18 = −1 * 18
2(5x − 3) − 3(4x + 3) − 18 = −18
10x − 6 − 12x − 9 − 18x = −18
10x − 12x − 18x = 6 + 9 − 18
−20x = −3

x = \frac{3}{20}

\frac{8 x - 5}{3} - \frac{4 x + 3}{4} + \frac{2 - 9 x}{2} = - 3

\frac{4 (8 x - 5) - 3 (4 x + 3) + 6 (2 - 9 x)}{12} = - 3

4(8x − 5) − 3(4x + 3) + 6(2 − 9x) = −3 * 12
32x − 20 − 12x − 9 + 12 − 54x = −36
32x − 12x − 54x = −36 + 20 + 9 − 12
−34x = −19

x = \frac{19}{34}

\frac{8 x^{2} - 3 x}{16} - \frac{6 x^{2} + 1}{12} = - 1

\frac{3 (8 x^{2} - 3 x) - 4 (6 x^{2} + 1)}{48} = - 1

3 (8 x^{2} - 3 x) - 4 (6 x^{2} + 1) = - 1 * 48

24 x^{2} - 9 x - 24 x^{2} - 4 = - 48

−9x = −48 + 4
−9x = −44

x = \frac{44}{9} = 4 \frac{8}{9}

ГДЗ Алгебра 7 класс Мерзляк, Полонский, Якир