Упр.514 Рабочая тетрадь №3 ГДЗ Мерзляк Полонский 6 класс (Математика)

1) 5/6 x + 8 = 1/4 x — 6; 2) 1,5(2x + 5) + x = 3(0,5x — 7) + 3,5;
3) 11/18 x — 2/9 = 5/12 x + 1 1/3; 4) 2/3 (4 1/2 x — 3/5) — 5/7 (7/15 x — 7/9) = -1 32/45.

1) $$\frac{5}{6}x+8=\frac{1}{4}x-6$$

$$\frac{5}{6}x-\frac{1}{4}x=-6-8$$
$$\frac{10}{12}x-\frac{3}{12}x=-14$$
$$\frac{7}{12}x=-14$$
$$x=-14:\frac{7}{12}=-14\cdot\frac{12}{7}=-24$$

Ответ: $$x=-24$$

2) $$1{,}5(2x+5)+x=3(0{,}5x-7)+3{,}5$$

$$3x+7{,}5+x=1{,}5x-21+3{,}5$$
$$4x+7{,}5=1{,}5x-17{,}5$$
$$4x-1{,}5x=-17{,}5-7{,}5$$
$$2{,}5x=-25$$
$$x=-25:2{,}5=-10$$

Ответ: $$x=-10$$

3) $$\frac{11}{18}x-\frac{2}{9}=\frac{5}{12}x+1\frac{1}{3}$$

$$\frac{11}{18}x-\frac{5}{12}x=1\frac{1}{3}+\frac{2}{9}$$
$$\frac{22}{36}x-\frac{15}{36}x=1\frac{1}{3}+\frac{2}{9}$$
$$\frac{7}{36}x=1\frac{5}{9}$$
$$\frac{7}{36}x=\frac{14}{9}$$
$$x=\frac{14}{9}:\frac{7}{36}=\frac{14}{9}\cdot\frac{36}{7}=8$$

Ответ: $$x=8$$

4) $$\frac{2}{3}\left(4\frac{1}{2}x-\frac{3}{5}\right)-\frac{5}{7}\left(\frac{7}{15}x-\frac{7}{9}\right)=-1\frac{32}{45}$$

$$\frac{2}{3}\left(\frac{9}{2}x-\frac{3}{5}\right)-\frac{5}{7}\left(\frac{7}{15}x-\frac{7}{9}\right)=-\frac{77}{45}$$
$$3x-\frac{2}{5}-\frac{1}{3}x+\frac{5}{9}=-\frac{77}{45}$$
$$\frac{8}{3}x-\frac{2}{5}+\frac{5}{9}=-\frac{77}{45}$$
$$\frac{8}{3}x-\frac{18}{45}+\frac{25}{45}=-\frac{77}{45}$$
$$\frac{8}{3}x+\frac{7}{45}=-\frac{77}{45}$$
$$\frac{8}{3}x=-\frac{77}{45}-\frac{7}{45}=-\frac{84}{45}$$
$$x=-\frac{84}{45}:\frac{8}{3}=-\frac{84}{45}\cdot\frac{3}{8}=-\frac{7}{5}=-0{,}7$$

Ответ: $$x=-0{,}7$$