Упр.553 ГДЗ Муравин 6 класс (Математика)

Задача

1) 0,6z-4,3=1,9z-0,9;
2) (2x-3)/(-0,5)=(-5x+6)/2;
3) 0,25-1/3 x=0,5x-1;
4) -1,7y=1,9y;
5)-0,7y-1 3/5=1,5y+0,4;
6) 2 2/3 :(y+1/3)=1 1/2 :(y-1 1/8).

Подробный ответ

1) $$0{,}6z-4{,}3=1{,}9z-0{,}9$$

$$0{,}6z-1{,}9z=-0{,}9+4{,}3$$
$$-1{,}3z=3{,}4$$
$$z=\frac{3{,}4}{-1{,}3}=-\frac{34}{13}=-2\frac{8}{13}$$

2) $$\frac{2x-3}{-0{,}5}=\frac{-5x+6}{2}$$

$$2(2x-3)=-0{,}5(-5x+6)$$
$$4x-6=2{,}5x-3$$
$$4x-2{,}5x=-3+6$$
$$1{,}5x=3$$
$$x=2$$

3) $$0{,}25-\frac{1}{3}x=0{,}5x-1$$

$$0{,}25+1=0{,}5x+\frac{1}{3}x$$
$$1{,}25=\frac{1}{2}x+\frac{1}{3}x$$
$$\frac{5}{4}=\frac{5}{6}x$$
$$x=\frac{5}{4}:\frac{5}{6}=\frac{5}{4}\cdot\frac{6}{5}=\frac{3}{2}=1{,}5$$

4) $$-1{,}7y=1{,}9y$$

$$-1{,}7y-1{,}9y=0$$
$$-3{,}6y=0$$
$$y=0$$

5) $$-0{,}7y-1\frac{3}{5}=1{,}5y+0{,}4$$

$$-0{,}7y-1{,}6=1{,}5y+0{,}4$$
$$-0{,}7y-1{,}5y=0{,}4+1{,}6$$
$$-2{,}2y=2$$
$$y=\frac{2}{-2{,}2}=-\frac{20}{22}=-\frac{10}{11}$$

6) $$2\frac{2}{3}:(y+\frac{1}{3})=1\frac{1}{2}:(y-1\frac{1}{8})$$

$$\frac{8}{3}:(y+\frac{1}{3})=\frac{3}{2}:(y-\frac{9}{8})$$
$$\frac{8}{3}\cdot\left(y-\frac{9}{8}\right)=\frac{3}{2}\cdot\left(y+\frac{1}{3}\right)$$
$$\frac{8}{3}y-3=\frac{3}{2}y+\frac{1}{2}$$
$$\frac{8}{3}y-\frac{3}{2}y=\frac{1}{2}+3$$
$$\frac{16-9}{6}y=\frac{7}{2}$$
$$\frac{7}{6}y=\frac{7}{2}$$
$$y=\frac{7}{2}:\frac{7}{6}=3$$