Упр.132 Рабочая тетрадь №1 ГДЗ Мерзляк Полонский 6 класс (Математика)

1) (x + 4/7) — 9/14 = 1/4; 3) 2 3/4 — (x — 3 1/8) = 1 1/6;
2) (x — 17/36) + 9/40 = 13/30; 4) 7 5/9 — (3 4/27 — x) = 2 5/6.

1) $$\left(x+\frac{4}{7}\right)-\frac{9}{14}=\frac{1}{4}$$

$$x+\frac{4}{7}=\frac{1}{4}+\frac{9}{14}$$
$$x+\frac{4}{7}=\frac{7}{28}+\frac{18}{28}=\frac{25}{28}$$
$$x=\frac{25}{28}-\frac{4}{7}=\frac{25}{28}-\frac{16}{28}=\frac{9}{28}$$

2) $$\left(x-\frac{17}{36}\right)+\frac{9}{40}=\frac{13}{30}$$

$$x-\frac{17}{36}=\frac{13}{30}-\frac{9}{40}$$
$$x-\frac{17}{36}=\frac{52}{120}-\frac{27}{120}=\frac{25}{120}=\frac{5}{24}$$
$$x=\frac{5}{24}+\frac{17}{36}=\frac{15}{72}+\frac{34}{72}=\frac{49}{72}$$

3) $$2\frac{3}{4}-\left(x-3\frac{1}{8}\right)=1\frac{1}{6}$$

$$x-3\frac{1}{8}=2\frac{3}{4}-1\frac{1}{6}$$
$$x-3\frac{1}{8}=2\frac{9}{12}-1\frac{2}{12}=1\frac{7}{12}$$
$$x=1\frac{7}{12}+3\frac{1}{8}$$
$$x=1\frac{14}{24}+3\frac{9}{24}=4\frac{23}{24}$$

4) $$7\frac{5}{9}-\left(3\frac{4}{27}-x\right)=2\frac{5}{6}$$

$$3\frac{4}{27}-x=7\frac{5}{9}-2\frac{5}{6}$$
$$3\frac{4}{27}-x=7\frac{10}{18}-2\frac{15}{18}=4\frac{13}{18}$$
$$x=3\frac{4}{27}-4\frac{13}{18}$$
$$x=3\frac{8}{54}-4\frac{39}{54}=-1\frac{31}{54}$$

Ответ

1) $$x=\frac{9}{28}$$; 2) $$x=\frac{49}{72}$$; 3) $$x=4\frac{23}{24}$$; 4) $$x=-1\frac{31}{54}$$.