Упр.865 ГДЗ Муравин 6 класс (Математика)

1)-0,21x-15/56=3/16+257/800 x;
2) 2/11 x+5/14=1,2+0,45x;
3) 3 1/3-2/3 x-1,7=3,9;
4) 2/3 (1/3 x-0,5)=4x+2,5;
5) 3/4 (0,5x+2/3)=3x+2 1/4;
6) 76-2,5x-4 7/25=8,28;
7) 6,76-2,2x=7 5/28-3 1/4;
8) 0,75x-1 2/3=1,5+0,2x.

1) $$-0{,}21x-\frac{15}{56}=\frac{3}{16}+\frac{257}{800}x$$

$$-\frac{21}{100}x-\frac{257}{800}x=\frac{3}{16}+\frac{15}{56}$$
$$-\frac{168}{800}x-\frac{257}{800}x=\frac{21}{112}+\frac{30}{112}$$
$$-\frac{425}{800}x=\frac{51}{112}$$
$$-\frac{17}{32}x=\frac{51}{112}$$
$$x=\frac{51}{112}:\left(-\frac{17}{32}\right)=-\frac{6}{7}$$

2) $$\frac{2}{11}x+\frac{5}{14}=1{,}2+0{,}45x$$

$$\frac{2}{11}x-\frac{45}{100}x=1{,}2-\frac{5}{14}$$
$$\frac{200}{1100}x-\frac{495}{1100}x=\frac{12}{10}-\frac{5}{14}$$
$$-\frac{295}{1100}x=\frac{84}{70}-\frac{25}{70}$$
$$-\frac{59}{220}x=\frac{59}{70}$$
$$x=\frac{59}{70}:\left(-\frac{59}{220}\right)=-\frac{22}{7}=-3\frac{1}{7}$$

3) $$3\frac{1}{3}-\frac{2}{3}x-1{,}7=3{,}9$$

$$-\frac{2}{3}x=3\frac{1}{3}-1{,}7-3{,}9$$
$$-\frac{2}{3}x=3\frac{1}{3}-5{,}6$$
$$-\frac{2}{3}x=3\frac{5}{15}-5\frac{9}{15}$$
$$-\frac{2}{3}x=-2\frac{4}{15}$$
$$x=-\frac{34}{15}:\frac{2}{3}=-\frac{34}{15}\cdot\frac{3}{2}=-\frac{17}{5}=-3{,}4$$

4) $$\frac{2}{3}\left(\frac{1}{3}x-0{,}5\right)=4x+2{,}5$$

$$\frac{2}{9}x-\frac{2}{3}\cdot\frac{1}{2}=4x+2{,}5$$
$$\frac{2}{9}x-\frac{1}{3}-4x=2\frac{1}{2}$$
$$-\frac{34}{9}x=2\frac{1}{2}+\frac{1}{3}$$
$$-\frac{34}{9}x=2\frac{5}{6}$$
$$x=\frac{17}{6}:\left(-\frac{34}{9}\right)=-\frac{3}{4}$$

5) $$\frac{3}{4}\left(0{,}5x+\frac{2}{3}\right)=3x+2\frac{1}{4}$$

$$\frac{3}{4}\cdot\frac{1}{2}x+\frac{1}{2}=3x+2\frac{1}{4}$$
$$\frac{3}{8}x+\frac{1}{2}-3x=2\frac{1}{4}$$
$$-\frac{21}{8}x=2\frac{1}{4}-\frac{1}{2}$$
$$-\frac{21}{8}x=1\frac{3}{4}$$
$$x=\frac{7}{4}:\left(-\frac{21}{8}\right)=-\frac{2}{3}$$

6) $$76-2{,}5x-4\frac{7}{25}=8{,}28$$

$$-2{,}5x=8{,}28-76+4\frac{7}{25}$$
$$-2{,}5x=8{,}28-76+4{,}28$$
$$-2{,}5x=-63{,}44$$
$$x=25{,}376$$

7) $$6{,}76-2{,}2x=7\frac{5}{28}-3\frac{1}{4}$$

$$-2{,}2x=7\frac{5}{28}-3\frac{1}{4}-6{,}76$$
$$-2{,}2x=7\frac{5}{28}-3\frac{7}{28}-6\frac{76}{100}$$
$$-2{,}2x=3\frac{26}{28}-6\frac{19}{25}$$
$$-2{,}2x=3\frac{13}{14}-6\frac{19}{25}$$
$$-\frac{11}{5}x=-2\frac{291}{350}$$
$$x=-2\frac{291}{350}:\left(-\frac{11}{5}\right)=\frac{991}{770}$$

8) $$0{,}75x-1\frac{2}{3}=1{,}5+0{,}2x$$

$$0{,}75x-0{,}2x=1\frac{1}{2}+1\frac{2}{3}$$
$$0{,}55x=1\frac{3}{6}+1\frac{4}{6}$$
$$\frac{55}{100}x=2\frac{7}{6}$$
$$x=\frac{19}{6}:\frac{55}{100}=\frac{19}{6}\cdot\frac{100}{55}=\frac{19}{6}\cdot\frac{20}{11}=\frac{190}{33}$$

Ответ

1) $$x=-\frac{6}{7}$$; 2) $$x=-3\frac{1}{7}$$; 3) $$x=-3{,}4$$; 4) $$x=-\frac{3}{4}$$; 5) $$x=-\frac{2}{3}$$; 6) $$x=25{,}376$$; 7) $$x=\frac{991}{770}$$; 8) $$x=\frac{190}{33}$$.