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

Решите уравнение.

1. $$\frac{5}{6}x+8=\frac{1}{4}x-6$$
2. $$1{,}5(2x+5)+x=3(0{,}5x-7)+3{,}5$$
3. $$\frac{11}{18}x-\frac{2}{9}=\frac{5}{12}x+1\frac{1}{3}$$
4. $$\frac{2}{3}\left(4\frac{1}{2}x-\frac{3}{5}\right)-\frac{5}{7}\left(\frac{7}{15}x-\frac{7}{9}\right)=-1\frac{32}{45}$$

1)

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

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)

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

Ответ: $$x=8$$.

4)

$$\frac{2}{3}\left(4\frac{1}{2}x-\frac{3}{5}\right)-\frac{5}{7}\left(\frac{7}{15}x-\frac{7}{9}\right)=-1\frac{32}{45}$$
$$\frac{2}{3}\cdot\frac{9}{2}x-\frac{2}{3}\cdot\frac{3}{5}-\frac{5}{7}\cdot\frac{7}{15}x+\frac{5}{7}\cdot\frac{7}{9}=-\frac{77}{45}$$
$$3x-\frac{2}{5}-\frac{1}{3}x+\frac{5}{9}=-\frac{77}{45}$$
$$2\frac{2}{3}x=-\frac{77}{45}+\frac{2}{5}-\frac{5}{9}$$
$$\frac{8}{3}x=-\frac{77}{45}+\frac{18}{45}-\frac{25}{45}$$
$$\frac{8}{3}x=-\frac{84}{45}$$
$$x=-\frac{84}{45}:\frac{8}{3}$$
$$x=-\frac{84}{45}\cdot\frac{3}{8}=-\frac{7}{10}=-0{,}7$$

Ответ: $$x=-0{,}7$$.