Упр.463 ГДЗ Мерзляк Полонский 6 класс (Математика)

1) 5*11/14x? 8/15= 5/21 ;
2) 7*3/10+ 25/28x=8*13/35 ;
3) 3*1/3?1*1/20x=1*14/15 ;
4) 3/8x+ 7/12x? 5/6x= 9/32 ;
5) 2*1/3:x?1*1/6=1 5/9 ;
6) 2*1/3:(x+1*1/6)=1*5/9 ;
7) 27:(31*3/7?2*11/14x)=1*1/8 ;
8) 48:(3*4/5x?25)=1*1/2.

1) $$5\frac{11}{14}x-\frac{8}{15}=\frac{5}{21}$$

$$5\frac{11}{14}=\frac{81}{14}$$

$$\frac{81}{14}x=\frac{5}{21}+\frac{8}{15}$$

$$\frac{81}{14}x=\frac{25}{105}+\frac{56}{105}=\frac{81}{105}$$

$$x=\frac{81}{105}\cdot\frac{14}{81}=\frac{2}{15}$$

2) $$7\frac{3}{10}+\frac{25}{28}x=8\frac{13}{35}$$

$$\frac{25}{28}x=8\frac{13}{35}-7\frac{3}{10}$$

$$\frac{25}{28}x=1\frac{26}{70}-\frac{21}{70}=1\frac{5}{70}=1\frac{1}{14}=\frac{15}{14}$$

$$x=\frac{15}{14}\cdot\frac{28}{25}=\frac{6}{5}=1\frac{1}{5}$$

3) $$3\frac{1}{3}-1\frac{1}{20}x=1\frac{14}{15}$$

$$1\frac{1}{20}x=3\frac{1}{3}-1\frac{14}{15}$$

$$\frac{21}{20}x=3\frac{5}{15}-1\frac{14}{15}=2\frac{20}{15}-1\frac{14}{15}=1\frac{6}{15}=1\frac{2}{5}=\frac{7}{5}$$

$$x=\frac{7}{5}\cdot\frac{20}{21}=\frac{4}{3}=1\frac{1}{3}$$

4) $$\frac{3}{8}x+\frac{7}{12}x-\frac{5}{6}x=\frac{9}{32}$$

$$\frac{9}{24}x+\frac{14}{24}x-\frac{20}{24}x=\frac{9}{32}$$

$$\frac{3}{24}x=\frac{9}{32}$$

$$\frac{1}{8}x=\frac{9}{32}$$

$$x=\frac{9}{32}\cdot 8=\frac{9}{4}=2\frac{1}{4}$$

5) $$2\frac{1}{3}:x-1\frac{1}{6}=1\frac{5}{9}$$

$$2\frac{1}{3}:x=1\frac{5}{9}+1\frac{1}{6}$$

$$\frac{7}{3}:x=1\frac{10}{18}+1\frac{3}{18}=2\frac{13}{18}=\frac{49}{18}$$

$$x=\frac{7}{3}:\frac{49}{18}=\frac{7}{3}\cdot\frac{18}{49}=\frac{6}{7}$$

6) $$2\frac{1}{3}:(x-1\frac{1}{6})=1\frac{5}{9}$$

$$x-1\frac{1}{6}=2\frac{1}{3}:1\frac{5}{9}$$

$$x-1\frac{1}{6}=\frac{7}{3}:\frac{14}{9}=\frac{7}{3}\cdot\frac{9}{14}=\frac{3}{2}$$

$$x=\frac{3}{2}+1\frac{1}{6}=\frac{9}{6}+\frac{7}{6}=\frac{16}{6}=\frac{8}{3}=2\frac{2}{3}$$

7) $$27:(31\frac{3}{7}-2\frac{11}{14}x)=1\frac{1}{8}$$

$$31\frac{3}{7}-2\frac{11}{14}x=27:1\frac{1}{8}$$

$$31\frac{3}{7}-2\frac{11}{14}x=27:\frac{9}{8}=27\cdot\frac{8}{9}=24$$

$$2\frac{11}{14}x=31\frac{3}{7}-24$$

$$\frac{39}{14}x=7\frac{3}{7}=\frac{52}{7}$$

$$x=\frac{52}{7}\cdot\frac{14}{39}=\frac{8}{3}=2\frac{2}{3}$$

8) $$48:(3\frac{4}{5}x-25)=1\frac{1}{2}$$

$$3\frac{4}{5}x-25=48:1\frac{1}{2}$$

$$\frac{19}{5}x-25=48:\frac{3}{2}=48\cdot\frac{2}{3}=32$$

$$\frac{19}{5}x=32+25=57$$

$$x=57\cdot\frac{5}{19}=15$$

Ответ

1) $$x=\frac{2}{15}$$; 2) $$x=1\frac{1}{5}$$; 3) $$x=1\frac{1}{3}$$; 4) $$x=2\frac{1}{4}$$; 5) $$x=\frac{6}{7}$$; 6) $$x=2\frac{2}{3}$$; 7) $$x=2\frac{2}{3}$$; 8) $$x=15$$.