Die ersten Gleichungen - Kantonsschule Solothurn
Die ersten Gleichungen - Kantonsschule Solothurn
Die ersten Gleichungen - Kantonsschule Solothurn
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<strong>Kantonsschule</strong> <strong>Solothurn</strong><br />
<strong>Die</strong> <strong>ersten</strong> <strong>Gleichungen</strong><br />
<strong>Gleichungen</strong><br />
RYS WS 08/09<br />
Bestimme x:<br />
1. 10 + x(2 – 3) = 8<br />
2. 10 + x(2 – 4) = 6<br />
3. 10 + x(2-5) = 4<br />
4. 10 + x(2- 6) = 2<br />
5. x – 3(2 – 3x) = 4<br />
6. x – 3(2 – 4x) = 7<br />
7. x – 3(2 -5x) = 2<br />
8. 2x – 3(4 – 6x) = 8<br />
9. 10 + 2(2x – 2) = 5<br />
10. 8 + 2(2x – 3) = 6<br />
11. 6 + 2(2x – 4) = 7<br />
12. 4 + 2(2x – 5) = 8<br />
13. 5 – 3(2x – 2) = 5<br />
14. 3 – 3(2x – 3) = 6<br />
15. 1 – 3(2x – 4) = 7<br />
16. -1 – 3(2x – 5) = 8<br />
17. 10 – 5(4 – 2x) = 40<br />
18. 20 – 5(4 – 2x) = 60<br />
19. 30 – 5(4 – 2x) = 80<br />
20. 40 – 5(4 – 2x) = 100<br />
21. -10(4 – 5x) = 5<br />
22. -12(1 – 5x) = 6<br />
23. -14(-2 – 5x) = 7<br />
24. -16(-5 – 5x) = 8<br />
25. x 2 = 4<br />
26. x 2 – 9 = 0<br />
27. x 2 = 2<br />
28. x 2 – 10 = 0<br />
29. x 2 = 20 2<br />
30. x 2 – x = 2<br />
Lösungen:<br />
1. x = 1 2. x = 1 3. x = 1 4. x = 1<br />
5. x = 1 6. x = 1 7. = 0.5 8. x = 1<br />
9. x = -0.25 10. x = 1 11. x = 9/4 12. x = 3.5<br />
13. x = 1 14. x = 1 15. x = 1 16. x = 1<br />
17. x = 5 18. x = 6 19. x = 7 20. x = 8<br />
21. x = 9/10 22. x = 3/10 23. x = -3/10 24. x = -9/10<br />
25. x = ±2 26. x = ±3 27. x = ± 2 28. x = ± 10<br />
29. x = 20 30 x = -1 oder x = 2<br />
1
Löse diese <strong>Gleichungen</strong>:<br />
31. (x + 4) 2 + (x – 6) 2 = 2x 2<br />
32. (2x + 3) 2 = 4x 2 + 45<br />
33. 21 = 25x 2 – (5x – 7) 2<br />
34. 5 + (x + 6) 2 = x(x – 4) – 7<br />
35. (5x – 6)(5x + 6) = (3x – 7) 2 + 4(2x + 1) 2 – 89<br />
36. 5(x – 7) = (x + 4) 2 – (x – 3)(x + 3)<br />
37. (x + 2)(2x – 9) + (x + 3) 2 = (2x – 1) 2 – (x + 5)(x – 5)<br />
38. 4(18x 2 – 9) + 2 = 2(7 – 6x)(7 + 6x)<br />
39. (x + 1) 2 + (x + 4) 2 + (x – 5) 2 = 3x(x + 2) – 1<br />
40. (9x – 2) 2 = (2 – 9x) 2<br />
41. (6 – 2x) 2 – (4 – x) 2 = 3x 2 – 16x + 20<br />
42. (5x – 9) 2 – (3x – 2) 2 = (7 – 4x) 2 – (7 + 4x) 2 – 8x(4 – 2x) + 6(x + 13)<br />
43. (5x – 1) 2 = (2 – 5x) 2<br />
44. (7x – 2) 2 = (2 – 7x) 2 + 1<br />
Lösungen<br />
31. x = 13 32. x = 3 33. x = 1 34. x = -3<br />
35. x = 0 36. x = -20 37. x = 7 38. x =<br />
39. x = 43/6 40. x ∈ R 41. x ∈ R 42. x = 1/60<br />
43. x = 3/10 44. ∅<br />
±<br />
11<br />
12<br />
2
<strong>Kantonsschule</strong> <strong>Solothurn</strong><br />
<strong>Gleichungen</strong><br />
RYS WS 08/09<br />
Etwas andere <strong>Gleichungen</strong><br />
45.<br />
x<br />
2<br />
=<br />
3<br />
5<br />
46.<br />
1<br />
x<br />
=<br />
1<br />
7<br />
47.<br />
1<br />
2 = ⋅ x<br />
4<br />
7<br />
48.<br />
3<br />
x<br />
=<br />
4<br />
8<br />
49. 1 = 4<br />
50.<br />
+ x<br />
2<br />
2<br />
=<br />
x<br />
1<br />
− x<br />
−<br />
3<br />
2<br />
51. 1 = 2<br />
52. x : 2 = 5 : 4<br />
53. (1 + x) : 3 = 4 : 6<br />
54. (1 + x) : x = 5 : 4<br />
55. x : (1 – x) = 2 : 3<br />
Lösungen<br />
45. x = 6/5 46. x = 7 47. x = 7/2 48. x = 6<br />
49. x = 6 50. x = - 4/3 51. x = - 1 52. x = 5/2<br />
53. x = 1 54. x = 4 55. x = 2/5<br />
3
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