מתמטיקה תיכונית/אלגברה תיכונית/משוואות/משוואות פשוטות בנעלם אחד/תרגילים/רמה ד

תרגילים

פתרו את המשוואות הבאות (מותר להשתמש במחשבון – המספרים גדולים):

1. $-{\frac {4}{3}}x-{\frac {2}{13}}x-{\frac {11}{6}}x-{\frac {1}{6}}x-{\frac {6}{11}}x={\frac {10}{9}}x+13x-{\frac {3}{10}}+{\frac {1}{4}}-{\frac {933897}{2860}}$
2. $-{\frac {3}{5}}x-{\frac {7}{9}}x-{\frac {7}{2}}-{\frac {11}{12}}x-{\frac {2}{7}}+{\frac {5}{7}}x=-{\frac {13}{7}}x-{\frac {13}{10}}x+{\frac {7}{3}}x-{\frac {2543}{420}}$
3. $-{\frac {3}{2}}x-{\frac {8}{13}}x-8x+{\frac {2}{7}}=-1-{\frac {10}{9}}+{\frac {5}{14}}x+{\frac {7}{4}}x-{\frac {1}{10}}+{\frac {1221679}{8190}}$
4. $-{\frac {11}{9}}-{\frac {5}{9}}x+{\frac {7}{3}}x+{\frac {5}{9}}x-{\frac {3}{5}}x-{\frac {9}{10}}=-{\frac {1}{6}}+{\frac {6}{7}}+{\frac {3}{13}}x+{\frac {43859}{4095}}$
5. ${\frac {3}{2}}-{\frac {14}{11}}-{\frac {5}{7}}x+{\frac {13}{8}}=7-{\frac {3}{5}}+{\frac {3}{10}}x+{\frac {5}{2}}+{\frac {1}{2}}+{\frac {2927}{440}}$
6. ${\frac {3}{5}}+2-{\frac {8}{7}}x=-{\frac {4}{3}}x+{\frac {1}{8}}x+x+13x+{\frac {9}{11}}x+{\frac {1}{3}}-{\frac {388001}{9240}}$
7. $-{\frac {1}{2}}x+{\frac {6}{5}}+{\frac {5}{12}}x-2+{\frac {4}{3}}+{\frac {3}{11}}x=-{\frac {2}{3}}x+{\frac {1}{6}}+{\frac {7}{3}}-{\frac {4123}{660}}$
8. ${\frac {1}{12}}+{\frac {7}{12}}x-{\frac {2}{3}}x-{\frac {13}{8}}-{\frac {13}{3}}x={\frac {6}{5}}x+{\frac {12}{5}}x+4-{\frac {7}{2}}+{\frac {913}{24}}$
9. ${\frac {3}{2}}-6x-{\frac {5}{6}}-{\frac {3}{5}}-{\frac {1}{2}}x+{\frac {7}{8}}={\frac {10}{9}}+{\frac {5}{7}}x+{\frac {9}{10}}x+{\frac {265397}{2520}}$
10. ${\frac {11}{6}}x+{\frac {3}{4}}x+{\frac {1}{2}}-{\frac {14}{11}}x+{\frac {11}{4}}=-{\frac {13}{3}}+2-7x-x+{\frac {5899}{66}}$
11. ${\frac {1}{7}}x+{\frac {1}{9}}x-{\frac {12}{7}}+2+{\frac {1}{2}}=-{\frac {5}{9}}x+{\frac {11}{5}}x-{\frac {14}{11}}x+{\frac {13}{4}}x+{\frac {110123}{1540}}$
12. ${\frac {1}{10}}x-{\frac {7}{10}}+{\frac {7}{5}}x+5x-{\frac {6}{11}}=-{\frac {5}{9}}x-{\frac {3}{4}}x-{\frac {14}{5}}x+{\frac {3}{2}}x+{\frac {8946}{55}}$
13. ${\frac {13}{5}}x+13x+{\frac {13}{14}}x+6=-{\frac {1}{10}}+{\frac {10}{13}}+{\frac {9}{13}}+{\frac {1}{3}}-{\frac {1}{2}}-{\frac {83687}{1365}}$
14. ${\frac {7}{4}}+1+{\frac {9}{8}}x-{\frac {1}{5}}+{\frac {13}{12}}x-11x={\frac {2}{3}}-{\frac {13}{11}}-4x-{\frac {116129}{1320}}$
15. ${\frac {7}{11}}x-{\frac {5}{13}}+{\frac {5}{4}}-1-x=2-{\frac {1}{2}}x+4x-11-{\frac {28079}{572}}$
16. $-{\frac {13}{7}}-{\frac {1}{7}}x+{\frac {3}{13}}x-{\frac {5}{7}}-{\frac {3}{4}}x-x={\frac {6}{5}}-{\frac {1}{2}}+{\frac {9}{2}}x+{\frac {4119}{455}}$
17. ${\frac {7}{8}}-{\frac {13}{9}}x-{\frac {2}{9}}-{\frac {2}{5}}x+x={\frac {13}{9}}+3-{\frac {10}{13}}-{\frac {1}{4}}x+{\frac {11977}{1560}}$
18. $-3-{\frac {13}{11}}-{\frac {12}{13}}x+{\frac {1}{2}}x+{\frac {11}{10}}-{\frac {4}{9}}x-{\frac {1}{14}}x={\frac {2}{11}}+{\frac {1}{7}}+{\frac {60983}{6930}}$
19. $-x+{\frac {9}{10}}x-13+{\frac {1}{9}}-{\frac {5}{13}}x-{\frac {13}{4}}={\frac {7}{8}}+1+{\frac {8}{11}}-{\frac {939847}{51480}}$
20. $-{\frac {2}{9}}+x+{\frac {10}{7}}+{\frac {4}{3}}x-1+{\frac {12}{11}}+{\frac {11}{7}}=-{\frac {10}{13}}+{\frac {2}{3}}+{\frac {51872}{1287}}$
21. $-{\frac {2}{5}}-{\frac {5}{2}}-7x+{\frac {13}{10}}x+{\frac {12}{11}}-3=-{\frac {13}{5}}x-{\frac {1}{11}}x-{\frac {7}{13}}+{\frac {2499}{1430}}$
22. ${\frac {1}{3}}+{\frac {4}{3}}x+{\frac {7}{6}}x+1+{\frac {9}{8}}+{\frac {2}{13}}x+3={\frac {7}{3}}+{\frac {1}{6}}+{\frac {17483}{312}}$
23. $-{\frac {1}{11}}x+{\frac {13}{8}}x+{\frac {6}{5}}x-{\frac {13}{14}}x-1=2x+{\frac {7}{6}}+{\frac {4}{3}}+{\frac {4}{7}}x+{\frac {1493}{440}}$
24. $-{\frac {3}{10}}x-{\frac {6}{7}}+{\frac {9}{2}}x+{\frac {5}{8}}x=-{\frac {5}{7}}x-{\frac {7}{4}}-{\frac {3}{11}}-{\frac {11}{13}}x+{\frac {6}{5}}x+{\frac {383059}{8008}}$
25. ${\frac {11}{10}}+{\frac {3}{5}}x-{\frac {7}{3}}x+{\frac {3}{8}}x={\frac {1}{12}}+{\frac {7}{4}}x-{\frac {8}{3}}x-{\frac {14}{13}}x-{\frac {13}{5}}-{\frac {38}{195}}$
26. $-3x-{\frac {3}{2}}+4+{\frac {5}{7}}x+5+{\frac {13}{2}}x+4x={\frac {4}{3}}-{\frac {3}{10}}x+{\frac {7411}{42}}$
27. ${\frac {2}{7}}x-{\frac {7}{2}}x-{\frac {13}{6}}+13x+{\frac {1}{8}}x={\frac {9}{10}}+{\frac {1}{4}}-{\frac {8}{9}}-{\frac {1}{11}}-{\frac {703007}{6930}}$
28. $-{\frac {5}{2}}-2x-{\frac {10}{7}}x+{\frac {13}{6}}+{\frac {5}{2}}x={\frac {4}{13}}x+{\frac {1}{8}}+{\frac {1}{3}}x-{\frac {5}{3}}x-{\frac {365}{2184}}$
29. $-{\frac {1}{2}}-{\frac {9}{8}}+{\frac {5}{4}}x+x+3=-2+x+{\frac {11}{7}}x+{\frac {9}{8}}+{\frac {99}{28}}$
30. $-11x+13x+{\frac {2}{9}}x+{\frac {2}{3}}+7={\frac {1}{9}}+{\frac {14}{5}}x+{\frac {4}{13}}-{\frac {5}{6}}+{\frac {1891}{234}}$
31. ${\frac {7}{6}}x+{\frac {13}{8}}x+{\frac {13}{14}}+2x=-5x+{\frac {2}{11}}+4x-{\frac {9}{2}}+9x-{\frac {5121}{154}}$
32. $-x-{\frac {1}{7}}-7x+{\frac {13}{4}}+{\frac {10}{7}}x-3={\frac {13}{10}}-{\frac {1}{4}}x-{\frac {1}{4}}x-{\frac {2717}{140}}$
33. ${\frac {7}{3}}-{\frac {4}{3}}-{\frac {4}{5}}x+{\frac {11}{4}}x-2x=5x+x+{\frac {14}{3}}x-1+{\frac {2602}{15}}$
34. ${\frac {7}{4}}x+{\frac {1}{3}}+{\frac {9}{14}}-1+1-{\frac {7}{9}}x-2x=-{\frac {3}{11}}+2+{\frac {10355}{1386}}$
35. ${\frac {3}{4}}-{\frac {2}{5}}x+{\frac {9}{4}}x+{\frac {5}{14}}x=-{\frac {1}{2}}+{\frac {6}{7}}x-{\frac {10}{9}}x-1+{\frac {1}{7}}+{\frac {18383}{630}}$
36. ${\frac {2}{3}}+{\frac {1}{14}}x-{\frac {3}{2}}+{\frac {1}{14}}x+{\frac {11}{5}}-{\frac {3}{13}}-{\frac {6}{11}}x=-{\frac {9}{4}}-{\frac {1}{11}}+{\frac {29831}{8580}}$
37. $-2x-{\frac {3}{5}}+{\frac {1}{3}}x-{\frac {4}{7}}x+{\frac {4}{3}}x+{\frac {11}{7}}x-{\frac {7}{12}}x={\frac {14}{5}}x-{\frac {7}{13}}+{\frac {10579}{260}}$
38. $-{\frac {5}{14}}x+{\frac {1}{2}}+{\frac {11}{13}}+{\frac {5}{8}}x=-{\frac {7}{6}}-{\frac {10}{11}}x-{\frac {1}{14}}+{\frac {3}{2}}-{\frac {1}{3}}-{\frac {17431}{1001}}$
39. ${\frac {2}{3}}-{\frac {13}{14}}+{\frac {7}{4}}+{\frac {6}{7}}x+6x=-{\frac {8}{7}}+{\frac {1}{5}}-x+{\frac {5}{2}}x-{\frac {1229}{420}}$
40. ${\frac {14}{13}}x-{\frac {9}{5}}x+{\frac {11}{2}}x-{\frac {2}{3}}-{\frac {1}{9}}x=-{\frac {1}{5}}+5x+{\frac {2}{3}}x-{\frac {1}{5}}x+{\frac {391}{1170}}$
41. ${\frac {11}{12}}x+{\frac {9}{10}}+{\frac {8}{9}}-{\frac {4}{5}}-11+{\frac {3}{14}}x-{\frac {13}{5}}+{\frac {1}{7}}x=-{\frac {5}{8}}-{\frac {8609}{504}}$
42. $-{\frac {9}{13}}x+{\frac {12}{5}}x-{\frac {2}{3}}-{\frac {9}{4}}x=-1+{\frac {1}{2}}-{\frac {10}{3}}x+{\frac {7}{11}}x-2x-{\frac {214597}{4290}}$
43. ${\frac {9}{10}}x-{\frac {1}{7}}+x-{\frac {12}{11}}-{\frac {3}{5}}={\frac {3}{4}}x+{\frac {2}{7}}x+{\frac {1}{3}}+{\frac {7}{5}}-{\frac {68389}{4620}}$
44. $2x-{\frac {11}{7}}+{\frac {1}{3}}x+x-{\frac {3}{2}}x-{\frac {12}{11}}={\frac {8}{13}}-{\frac {3}{11}}+{\frac {5}{9}}x+{\frac {107017}{18018}}$
45. ${\frac {1}{10}}+{\frac {8}{9}}x-{\frac {12}{11}}x+{\frac {5}{6}}x-7x-{\frac {2}{9}}x+{\frac {3}{4}}=-{\frac {5}{11}}+{\frac {8}{5}}x+{\frac {2089}{220}}$
46. ${\frac {12}{11}}+{\frac {2}{7}}+{\frac {1}{8}}x+{\frac {11}{14}}+x-{\frac {5}{3}}+{\frac {5}{7}}-{\frac {3}{5}}={\frac {1}{6}}-{\frac {50951}{2310}}$
47. $-{\frac {10}{13}}x-{\frac {11}{13}}x-{\frac {7}{13}}-14=-{\frac {5}{4}}x+{\frac {14}{5}}x-7x+x-{\frac {1}{6}}x-{\frac {37091}{780}}$
48. $-{\frac {13}{14}}+{\frac {6}{5}}x+2x+{\frac {11}{4}}x+7=-{\frac {13}{8}}x+{\frac {7}{8}}x+{\frac {7}{2}}+{\frac {1}{5}}+{\frac {1959}{35}}$
49. $-{\frac {13}{6}}x-{\frac {10}{3}}+{\frac {11}{2}}-{\frac {3}{8}}-1=-9-{\frac {9}{7}}x+{\frac {3}{2}}-x+{\frac {1373}{168}}$
50. ${\frac {11}{7}}+{\frac {1}{14}}-9x-{\frac {7}{13}}-x-7x+{\frac {12}{13}}x-{\frac {5}{6}}x=-{\frac {1}{5}}x+{\frac {185491}{2730}}$

תשובות סופיות

1. $18$
2. $3$
3. $-12$
4. $9$
5. $-14$
6. $3$
7. $-5$
8. $-5$
9. $-13$
10. $9$
11. $-21$
12. $18$
13. $-4$
14. $19$
15. $15$
16. $-2$
17. $-18$
18. $-13$
19. $-1$
20. $16$
21. $-2$
22. $20$
23. $-9$
24. $9$
25. $-6$
26. $20$
27. $-10$
28. $3$
29. $-4$
30. $0$
31. $12$
32. $3$
33. $-16$
34. $-8$
35. $11$
36. $0$
37. $-15$
38. $-16$
39. $-1$
40. $-1$
41. $-4$
42. $-12$
43. $-13$
44. $7$
45. $-1$
46. $-20$
47. $-11$
48. $8$
49. $-1$
50. $-4$