Упр.845 ГДЗ Муравин 6 класс (Математика)

1. Решите уравнение:
   1) $$15\frac{4}{7}-4\frac{3}{8}\cdot\left(1\frac{3}{7}-x\right)=13\frac{4}{7}$$;
   2) $$\frac{21}{25}\cdot\frac{5}{7}-\frac{3}{16}x=\frac{11}{20}$$;
   3) $$\left(x-1\frac{1}{3}\right)\mathbin{\colon}1\frac{5}{12}=\frac{4}{51}$$;
   4) $$\left(4x+3\frac{5}{8}\right)\cdot\frac{4}{9}=2\frac{1}{2}$$.

1) $$15\frac{4}{7}-4\frac{3}{8}\cdot\left(1\frac{3}{7}-x\right)=13\frac{4}{7}$$

Перенесём число $$13\frac{4}{7}$$ в левую часть:

$$4\frac{3}{8}\cdot\left(1\frac{3}{7}-x\right)=15\frac{4}{7}-13\frac{4}{7}=2$$

$$4\frac{3}{8}=\frac{35}{8}, \quad 1\frac{3}{7}=\frac{10}{7}$$

$$\frac{35}{8}\left(\frac{10}{7}-x\right)=2$$

$$\frac{10}{7}-x=2:\frac{35}{8}=2\cdot\frac{8}{35}=\frac{16}{35}$$

$$x=\frac{10}{7}-\frac{16}{35}=\frac{50}{35}-\frac{16}{35}=\frac{34}{35}$$

2) $$\frac{21}{25}\cdot\frac{5}{7}-\frac{3}{16}x=\frac{11}{20}$$

$$\frac{21}{25}\cdot\frac{5}{7}=\frac{3}{5}$$

$$\frac{3}{5}-\frac{3}{16}x=\frac{11}{20}$$

$$\frac{3}{16}x=\frac{3}{5}-\frac{11}{20}=\frac{12}{20}-\frac{11}{20}=\frac{1}{20}$$

$$x=\frac{1}{20}:\frac{3}{16}=\frac{1}{20}\cdot\frac{16}{3}=\frac{4}{15}$$

3) $$\left(x-1\frac{1}{3}\right):1\frac{5}{12}=\frac{4}{51}$$

$$x-1\frac{1}{3}=\frac{4}{51}\cdot1\frac{5}{12}$$

$$1\frac{5}{12}=\frac{17}{12}$$

$$x-1\frac{1}{3}=\frac{4}{51}\cdot\frac{17}{12}=\frac{1}{9}$$

$$x=\frac{1}{9}+1\frac{1}{3}=\frac{1}{9}+\frac{4}{3}=\frac{1}{9}+\frac{12}{9}=\frac{13}{9}=1\frac{4}{9}$$

4) $$\left(4x+3\frac{5}{8}\right)\cdot\frac{4}{9}=2\frac{1}{2}$$

$$4x+3\frac{5}{8}=2\frac{1}{2}:\frac{4}{9}=\frac{5}{2}\cdot\frac{9}{4}=\frac{45}{8}$$

$$4x=\frac{45}{8}-3\frac{5}{8}=\frac{45}{8}-\frac{29}{8}=\frac{16}{8}=2$$

$$x=2:4=\frac{1}{2}$$

Ответ

1) $$x=\frac{34}{35}$$; 2) $$x=\frac{4}{15}$$; 3) $$x=1\frac{4}{9}$$; 4) $$x=\frac{1}{2}$$.