Упр.386 Часть 2 ГДЗ Дорофеев Петерсон 5 класс (Математика)

1) 3x + 5x = 7; 5) 3 1/8 : (x — 4 7/24) = 17/18 + 1 5/6;
2) 1 = 6x — 2x + x; 6) 24 1/14 + 8 3/7 = (x : 1 1/9) · 5 5/12;
3) 7 1/4x — x = 9 3/8; 7) (4 1/5 : x + 1 1/3) : 2 4/35 — 4/5 = 1 8/15;
4) 1 : 2 7/9 = x + 4 2/5 x; 8) 4 1/5 : 1 1/5 = 2 3/4 · 4 — 1 7/18 x.

1) $$3x+5x=7$$

$$8x=7$$
$$x=\frac{7}{8}$$

2) $$1=6x-2x+x$$

$$1=5x$$
$$x=\frac{1}{5}$$

3) $$7\frac{1}{4}x-x=9\frac{3}{8}$$

$$6\frac{1}{4}x=9\frac{3}{8}$$
$$\frac{25}{4}x=\frac{75}{8}$$
$$x=\frac{75}{8}:\frac{25}{4}=\frac{75}{8}\cdot\frac{4}{25}=\frac{3}{2}$$

4) $$1:2\frac{7}{9}=x+4\frac{2}{5}x$$

$$1:\frac{25}{9}=5\frac{2}{5}x$$
$$\frac{9}{25}=\frac{27}{5}x$$
$$x=\frac{9}{25}:\frac{27}{5}=\frac{9}{25}\cdot\frac{5}{27}=\frac{1}{15}$$

5) $$3\frac{1}{8}:(x-4\frac{7}{24})=\frac{17}{18}+1\frac{5}{6}$$

$$\frac{25}{8}:(x-4\frac{7}{24})=\frac{17}{18}+\frac{11}{6}$$
$$\frac{25}{8}:(x-4\frac{7}{24})=\frac{17}{18}+\frac{33}{18}$$
$$\frac{25}{8}:(x-4\frac{7}{24})=\frac{50}{18}=\frac{25}{9}$$
$$x-4\frac{7}{24}=\frac{25}{8}:\frac{25}{9}=\frac{25}{8}\cdot\frac{9}{25}=\frac{9}{8}=1\frac{1}{8}$$
$$x=1\frac{1}{8}+4\frac{7}{24}=5\frac{5}{12}$$

6) $$24\frac{1}{14}+8\frac{3}{7}=(x:1\frac{1}{9})\cdot5\frac{5}{12}$$

$$24\frac{1}{14}+8\frac{3}{7}=32\frac{1}{2}$$
$$x:\frac{10}{9}\cdot\frac{65}{12}=32\frac{1}{2}$$
$$x:\frac{10}{9}=\frac{65}{12}^{-1}\cdot32\frac{1}{2}$$

Удобнее записать так:

$$\left(x:\frac{10}{9}\right)\cdot\frac{65}{12}=32\frac{1}{2}$$
$$x:\frac{10}{9}=32\frac{1}{2}:\frac{65}{12}$$
$$x:\frac{10}{9}= \frac{65}{2}\cdot\frac{12}{65}=6$$
$$x=6\cdot\frac{10}{9}=\frac{20}{3}=6\frac{2}{3}$$

7) $$\left(4\frac{1}{5}:x+1\frac{1}{3}\right):2\frac{4}{35}-\frac{4}{5}=1\frac{8}{15}$$

$$\left(4\frac{1}{5}:x+1\frac{1}{3}\right):\frac{74}{35}=1\frac{8}{15}+\frac{4}{5}$$
$$\left(4\frac{1}{5}:x+1\frac{1}{3}\right):\frac{74}{35}=2\frac{1}{3}$$
$$4\frac{1}{5}:x+1\frac{1}{3}=2\frac{1}{3}\cdot\frac{74}{35}=\frac{74}{15}$$
$$4\frac{1}{5}:x=\frac{74}{15}-1\frac{1}{3}=\frac{74}{15}-\frac{20}{15}=\frac{54}{15}=3\frac{3}{5}$$
$$x=4\frac{1}{5}:3\frac{3}{5}=\frac{21}{5}:\frac{18}{5}=\frac{21}{18}=\frac{7}{6}=1\frac{1}{6}$$

8) $$4\frac{1}{5}:1\frac{1}{5}=2\frac{3}{4}\cdot4-1\frac{7}{18}x$$

$$\frac{21}{5}:\frac{6}{5}=11-1\frac{7}{18}x$$
$$\frac{21}{5}\cdot\frac{5}{6}=11-1\frac{7}{18}x$$
$$\frac{7}{2}=11-1\frac{7}{18}x$$
$$1\frac{7}{18}x=11-\frac{7}{2}=7\frac{1}{2}$$
$$x=7\frac{1}{2}:1\frac{7}{18}=\frac{15}{2}:\frac{25}{18}=\frac{15}{2}\cdot\frac{18}{25}=\frac{27}{5}=5\frac{2}{5}$$

Ответ

1) $$x=\frac{7}{8}$$; 2) $$x=\frac{1}{5}$$; 3) $$x=\frac{3}{2}$$; 4) $$x=\frac{1}{15}$$; 5) $$x=5\frac{5}{12}$$; 6) $$x=6\frac{2}{3}$$; 7) $$x=1\frac{1}{6}$$; 8) $$x=5\frac{2}{5}$$.