No п/п Уравнения Уравнения 1 y: 51,611,2: 34,4 19 2x4 3 2 y:34:2 20 3 7 = 5x 3 14:1526: x 2132 4 0,5x: 516: 0,8 22 12 21 14 2114 5 25 y:= 20 23 3 6 12,37x 24 21 49 4,2 = 2550x 7 5:3=5x 25 25 12 18x 13 39 1339 8 26 12,3 7x = 60 4,2 9 27 0,2:(x-2)=:2 = 5 10 x:5=7:2 28 2 5x-2 11 29 6 = 48x 2x+3 51 12 30 x+1,2 8,5 = 2,4 6,8 x:= 13 31 3,6 7,8 = x-1,2 6,5 1:x=4:20 14 2,8: 3,22,1: x 32 3x-2 0,5 = 1,8 9 15 3:2=2:x 16 25 45 72.2 X:18 17 35 7:24: y 3:1 = 2y 18 39,1: x = 18,63: 40,5 36 1:x=5:2

Математика. 5-9 класс.

Привет! Давай решим эти уравнения вместе. Будем двигаться по порядку.

1. №1

   \[y : 51.6 = 11.2 : 34.4\]

   \[y = \frac{51.6 \cdot 11.2}{34.4}\]

   \[y = \frac{577.92}{34.4}\]

   \[y = 16.8\]

2. №2

   \[y : 3\frac{1}{5} = 4\frac{1}{2} : 2\frac{1}{4}\]

   \[y : \frac{16}{5} = \frac{9}{2} : \frac{9}{4}\]

   \[y : \frac{16}{5} = \frac{9}{2} \cdot \frac{4}{9}\]

   \[y : \frac{16}{5} = 2\]

   \[y = 2 \cdot \frac{16}{5}\]

   \[y = \frac{32}{5}\]

   \[y = 6.4\]

3. №3

   \[14 : 15 = 26 : x\]

   \[x = \frac{15 \cdot 26}{14}\]

   \[x = \frac{390}{14}\]

   \[x = \frac{195}{7}\]

   \[x \approx 27.86\]

4. №4

   \[0.5x : 5 = 16 : 0.8\]

   \[0.5x = \frac{5 \cdot 16}{0.8}\]

   \[0.5x = \frac{80}{0.8}\]

   \[0.5x = 100\]

   \[x = \frac{100}{0.5}\]

   \[x = 200\]

5. №5

   \[y : \frac{25}{6} = \frac{4}{7} : \frac{20}{21}\]

   \[y = \frac{25}{6} \cdot \frac{4}{7} : \frac{20}{21}\]

   \[y = \frac{25}{6} \cdot \frac{4}{7} \cdot \frac{21}{20}\]

   \[y = \frac{25 \cdot 4 \cdot 21}{6 \cdot 7 \cdot 20}\]

   \[y = \frac{2100}{840}\]

   \[y = 2.5\]

6. №6

   \[\frac{12.3}{6} = \frac{7x}{4.2}\]

   \[7x = \frac{12.3 \cdot 4.2}{6}\]

   \[7x = \frac{51.66}{6}\]

   \[7x = 8.61\]

   \[x = \frac{8.61}{7}\]

   \[x = 1.23\]

7. №7

   \[5\frac{3}{5} : 3\frac{1}{2} = 5\frac{1}{4} : x\]

   \[\frac{28}{5} : \frac{7}{2} = \frac{21}{4} : x\]

   \[x = \frac{\frac{7}{2} \cdot \frac{21}{4}}{\frac{28}{5}}\]

   \[x = \frac{7 \cdot 21 \cdot 5}{2 \cdot 4 \cdot 28}\]

   \[x = \frac{735}{224}\]

   \[x = 3.28125\]

8. №8

   \[\frac{x}{2} = \frac{3}{7}\]

   \[x = \frac{2 \cdot 3}{7}\]

   \[x = \frac{6}{7}\]

9. №9

   \[\frac{15}{x} = \frac{5}{8}\]

   \[x = \frac{15 \cdot 8}{5}\]

   \[x = \frac{120}{5}\]

   \[x = 24\]

10. №10

    \[x : 5 = 7 : \frac{1}{2}\]

    \[x = \frac{5 \cdot 7}{\frac{1}{2}}\]

    \[x = 5 \cdot 7 \cdot 2\]

    \[x = 70\]

11. №11

    \[\frac{48}{51} = \frac{x}{34}\]

    \[x = \frac{48 \cdot 34}{51}\]

    \[x = \frac{1632}{51}\]

    \[x = 32\]

12. №12

    \[x : \frac{1}{3} = 3\frac{1}{4} : 2\frac{1}{2}\]

    \[x : \frac{1}{3} = \frac{13}{4} : \frac{5}{2}\]

    \[x = \frac{1}{3} \cdot \frac{13}{4} : \frac{5}{2}\]

    \[x = \frac{1}{3} \cdot \frac{13}{4} \cdot \frac{2}{5}\]

    \[x = \frac{26}{60}\]

    \[x = \frac{13}{30}\]

13. №13

    \[1\frac{1}{2} : x = 4\frac{3}{8} : 2\frac{3}{8}\]

    \[\frac{3}{2} : x = \frac{35}{8} : \frac{19}{8}\]

    \[x = \frac{\frac{3}{2} \cdot \frac{19}{8}}{\frac{35}{8}}\]

    \[x = \frac{3 \cdot 19 \cdot 8}{2 \cdot 8 \cdot 35}\]

    \[x = \frac{456}{560}\]

    \[x = \frac{57}{70}\]

14. №14

    \[2.8 : 3.2 = 2.1 : x\]

    \[x = \frac{3.2 \cdot 2.1}{2.8}\]

    \[x = \frac{6.72}{2.8}\]

    \[x = 2.4\]

15. №15

    \[3\frac{1}{8} : 2 = 2\frac{2}{3} : x\]

    \[\frac{25}{8} : 2 = \frac{8}{3} : x\]

    \[x = \frac{2 \cdot \frac{8}{3}}{\frac{25}{8}}\]

    \[x = \frac{2 \cdot 8 \cdot 8}{3 \cdot 25}\]

    \[x = \frac{128}{75}\]

    \[x \approx 1.71\]

16. №16

    \[x : \frac{7}{18} = \frac{2}{3} : \frac{7}{9}\]

    \[x = \frac{7}{18} \cdot \frac{2}{3} : \frac{7}{9}\]

    \[x = \frac{7}{18} \cdot \frac{2}{3} \cdot \frac{9}{7}\]

    \[x = \frac{126}{378}\]

    \[x = \frac{1}{3}\]

17. №17

    \[3\frac{3}{4} : 1\frac{1}{8} = 2\frac{1}{3} : y\]

    \[\frac{15}{4} : \frac{9}{8} = \frac{7}{3} : y\]

    \[y = \frac{\frac{9}{8} \cdot \frac{7}{3}}{\frac{15}{4}}\]

    \[y = \frac{9 \cdot 7 \cdot 4}{8 \cdot 3 \cdot 15}\]

    \[y = \frac{252}{360}\]

    \[y = 0.7\]

18. №18

    \[39.1 : x = 18.63 : 40.5\]

    \[x = \frac{39.1 \cdot 40.5}{18.63}\]

    \[x = \frac{1583.55}{18.63}\]

    \[x = 85\]

19. №19

    \[\frac{2x}{3} = \frac{4}{9}\]

    \[2x = \frac{4 \cdot 3}{9}\]

    \[2x = \frac{12}{9}\]

    \[2x = \frac{4}{3}\]

    \[x = \frac{4}{3} : 2\]

    \[x = \frac{4}{3} \cdot \frac{1}{2}\]

    \[x = \frac{2}{3}\]

20. №20

    \[\frac{3}{5} = \frac{7}{x}\]

    \[x = \frac{5 \cdot 7}{3}\]

    \[x = \frac{35}{3}\]

    \[x \approx 11.67\]

21. №21

    \[\frac{x}{16} = \frac{9}{32}\]

    \[x = \frac{16 \cdot 9}{32}\]

    \[x = \frac{144}{32}\]

    \[x = 4.5\]

22. №22

    \[\frac{12}{21} = \frac{x}{14}\]

    \[x = \frac{12 \cdot 14}{21}\]

    \[x = \frac{168}{21}\]

    \[x = 8\]

23. №23

    \[\frac{2x}{3} = \frac{4}{9}\]

    \[2x = \frac{4 \cdot 3}{9}\]

    \[2x = \frac{12}{9}\]

    \[2x = \frac{4}{3}\]

    \[x = \frac{4}{3} : 2\]

    \[x = \frac{4}{3} \cdot \frac{1}{2}\]

    \[x = \frac{2}{3}\]

24. №24

    \[\frac{21}{x} = \frac{49}{25}\]

    \[x = \frac{21 \cdot 25}{49}\]

    \[x = \frac{525}{49}\]

    \[x = \frac{75}{7}\]

25. №25

    \[\frac{12}{50x} = \frac{13}{18x}\]

    \[12 \cdot 18x = 13 \cdot 50x\]

    \[216x = 650x\]

    \[650x - 216x = 0\]

    \[434x = 0\]

    \[x = 0\]

26. №26

    \[\frac{12.3}{60} = \frac{7x}{4.2}\]

    \[7x = \frac{12.3 \cdot 4.2}{60}\]

    \[7x = \frac{51.66}{60}\]

    \[7x = 0.861\]

    \[x = \frac{0.861}{7}\]

    \[x = 0.123\]

27. №27

    \[0.2 : (x - 2) = \frac{1}{2} : 2\]

    \[0.2 : (x - 2) = \frac{1}{4}\]

    \[x - 2 = \frac{0.2}{\frac{1}{4}}\]

    \[x - 2 = 0.2 \cdot 4\]

    \[x - 2 = 0.8\]

    \[x = 2.8\]

28. №28

    \[\frac{2}{5x - 2} = \frac{5}{7}\]

    \[5(5x - 2) = 2 \cdot 7\]

    \[25x - 10 = 14\]

    \[25x = 24\]

    \[x = \frac{24}{25}\]

29. №29

    \[\frac{6}{2x + 3} = \frac{5}{7}\]

    \[5(2x + 3) = 6 \cdot 7\]

    \[10x + 15 = 42\]

    \[10x = 27\]

    \[x = 2.7\]

30. №30

    \[\frac{x + 1.2}{2.4} = \frac{8.5}{6.8}\]

    \[x + 1.2 = \frac{8.5 \cdot 2.4}{6.8}\]

    \[x + 1.2 = \frac{20.4}{6.8}\]

    \[x + 1.2 = 3\]

    \[x = 1.8\]

31. №31

    \[\frac{3.6}{x - 1.2} = \frac{7.8}{6.5}\]

    \[7.8(x - 1.2) = 3.6 \cdot 6.5\]

    \[7.8x - 9.36 = 23.4\]

    \[7.8x = 32.76\]

    \[x = 4.2\]

32. №32

    \[\frac{3x - 2}{1.8} = \frac{0.5}{9}\]

    \[9(3x - 2) = 1.8 \cdot 0.5\]

    \[27x - 18 = 0.9\]

    \[27x = 18.9\]

    \[x = 0.7\]

33. №33

    \[\frac{5.2}{8} = \frac{1.5}{5x + 1}\]

    \[5.2(5x + 1) = 8 \cdot 1.5\]

    \[26x + 5.2 = 12\]

    \[26x = 6.8\]

    \[x = \frac{6.8}{26}\]

34. №34

    \[x : \frac{4}{25} = \frac{3}{4} : \frac{4}{5}\]

    \[x = \frac{4}{25} \cdot \frac{3}{4} : \frac{4}{5}\]

    \[x = \frac{4}{25} \cdot \frac{3}{4} \cdot \frac{5}{4}\]

    \[x = \frac{60}{400}\]

    \[x = 0.15\]

35. №35

    \[7\frac{4}{5} : 2\frac{3}{5} = 4\frac{1}{2} : y\]

    \[\frac{39}{5} : \frac{13}{5} = \frac{9}{2} : y\]

    \[y = \frac{\frac{13}{5} \cdot \frac{9}{2}}{\frac{39}{5}}\]

    \[y = \frac{13 \cdot 9 \cdot 5}{5 \cdot 2 \cdot 39}\]

    \[y = \frac{585}{390}\]

    \[y = 1.5\]

36. №36

    \[1\frac{7}{9} : x = 5\frac{4}{9} : 2\frac{5}{8}\]

    \[\frac{16}{9} : x = \frac{49}{9} : \frac{21}{8}\]

    \[x = \frac{\frac{16}{9} \cdot \frac{21}{8}}{\frac{49}{9}}\]

    \[x = \frac{16 \cdot 21 \cdot 9}{9 \cdot 8 \cdot 49}\]

    \[x = \frac{3024}{3528}\]

    \[x = 0.857\]

Ответ: Выше приведены решения уравнений.

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