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FACOLTA DI FARMACIA E BIOLOGIA
CORSO DI LAUREA IN BIOLOGIA
CORSO DI RIALLINEAMENTO IN MATEMATICA
Equazioni di primo grado
1. 2(3x− 1) = 3x+ 7
2. 3(x− 1)− 2x = 4(x− 2)− 1
3. 3x+ 2(x− 1) = 5x− 3
4. 4(2− x) + 3x− 1 = −(x+ 2) + 9
5. 2(x− 3) = 4(1− 2x) + 3(x− 1)
6. 2(3x− 7) = 3(1− x)− 8x
7. 6(x+ 2)− 3(x+ 4) + 3 = 2x+ 4(x+ 1)
8. 3(x+ 2)− (2x+ 1) = 10− 3(x− 1)− 4x
9. 2(x− 3)− 5(1 + x)− 1 = x+ 2(1− x)
10. 5 + 2(4− x) + 3(x− 5) = 6(x+ 2)− 3(4x− 7)
11. 1− [2− 3(x− 1) + x] = 2x− 4(x+ 1)
12. 3− 2(x+ 2)− (1 + 4x) = x− 2(2x+ 1)
13. 2− [2x− (3− x)− 4] = 3(1− 2x) + 2− 3x
14. x+ 10 + 2(3x− 5) = −(3x− 1) + 6(1 + 3x) + 1
15. 5− [−(x− 1− 5(2x− 1))] = 2 + x+ 5(2x− 3)
16. x− 1 + 5(x− 3) + 4 = 6(x− 2)
17. 13(x− 3) + 1 = 2
(12x− 1
)+ 4x
3
18.(13− 1
2
)4x− 1
2(1− 6x) + 2x
3= 0
19. 12(x− 1) + 1
4(x+ 1) + x(1
2− 2) = 1− 2x
20. (3x+ 1)(12− 1)+ 1
2(x+ 1) = −x
21. (2x− 1)(13− 1
2
)+ 1
2x = 4 + x
6
22. 13
(2x+12− x−1
4
)− 1
2
(x+13− x
2
)= x− 5
4
2
Equazioni di secondo grado
1. x2 − 16 = 0
2. 3x2 − 27 = 0
3. x2 + 1 = 0
4. x2
4− 1 = 0
5. (2x− 1)2 − (x2 − 1) + 4x = 14
6. 3(2x+5)8− 2x2 = 3x−5
4
7. (x− 1)(x+ 2) + (x− 3)(x+ 1) = (x− 2)(x+ 1)
8. x2 − 8x = 0
9. 3x2 + 5x = 0
10. −x2 − 3x = 0
11. 2x = 52x2
12. (x− 1)2 − 1 = x
13. (x+ 2)2 − 3x = 4
14. (x+ 2)2 = 3(x− 1)2 + 1
15. 2 + (x+ 2)2 = 5x+ 3(2− x)
16. x2 − 7x+ 10 = 0
17. x2 + x− 6 = 0
18. x2 + x+ 3 = 0
19. x2 − 4x− 5 = 0
20. x2 − 12x+ 36 = 0
21. 2x2 − 9x+ 9 = 0
22. 4x2 + 4x+ 1 = 0
23. 2x2 − 2x+ 3 = 0
3
24. x2
4− x+ 7
6
25. x(x2 − 3x) + 2 = x3
26. (x+ 1)2 + (x+ 2)2 − 41 = 0
27. (2x− 1)2 = x2 + 12
28. x− 3 + x(x+ 3) = 2x2 + 1
29. 3(x2 − 1) + 8x(1− x) = (1− 2x)2
30. (2x+ 1)2 + (x+ 2)(x+ 1) = x+ 2
31. 2− 3x(4− x) = x2 − 16
32. 3x−54− x−3
5= 17+x2
20
33. (x+1)2
3− 2x
3= 1−x
2+ 2
3
34. x2−43
+ (x−1)22
= 7x2+512
35. (2− x)(7− x) = 83x− x2+28
6
36. (2x−1)23− (x−2)(1−2x)
6= (1− 2x)2
37. (x+2)(5x+3)4
= (x+1)(x−1)4
+ (x+1)(2−x)2
38. x8+ 1+x
4= x2+12x
32− 1
4
39. x2+115
+ 5x−15
+ (x+2)(2−x)3
+ 3(x−2)5
40. (x+ 1)3 + (x−1)(2−x)2
= (x2 − 1)x
4
Equazioni frazionarie
1. 3x+ 5 = 0
2. 1x+ 1
6= −2
3
3. 1x+3
+ 2 = 0
4. xx+1
= 2x+1x− 1
5. 2x−2 = 5
x+3− 1
2−x
6. 5xx+6− 2 = 2x− 1− x(2x+3)
x+6
7. x2−1x+1− 2(x+ 3) = 0
8. 3x+2
+ 52−x = 0
9. 16− 1
1−x = 1+x2−2x
10. 4+x3
= 5x+ 1 + 1−x
6
11. 2x+1
+ 1− 1x−1 = 8
x2−1
12. 12x−1 −
2x= x− 2
x(x+ 1)
13. xx−6 −
x−16
= 23+ x+6
6−x
14. 11−x −
43= x
x+1− 1+x
x−1
15. 1x−1 = 5
x2− 3
x2−x
16. xx−1 +
5−2xx2−3x+2
+ 1x−2 = 0
17. x2−4x+6x2−3x+2
− 27x−2 = 1− 26+x
x−1
18. 2x+1x−5 + 3x−1
x−3 = 64x2−8x+15
19. 4x+32x−1 +
8x−14x+2
= 474x2−1
20. 2x−1 = 3
4+ 2
x2−1
5
Equazioni di grado superiore al secondo
1. (x2 − 2x)(3x+ 6) = 0
2. (x2 − 3x)(x2 + 4x) = 0
3. x3 − 5x2 + 6x = 0
4. 2x3 + x2 − x = 0
5. 3x3 − 2x2 + x = 0
6. x3 + 5x2 + 3x− 9 = 0
7. x3 + 7x2 + 15x+ 9 = 0
8. 4x4 − x2 = 0
9. 16x4 − 1 = 0
10. x4 + 5x3 + 5x2 − 5x− 6 = 0
11. 8x4 − 16x3 + x− 2 = 0
12. x3 − 5x2 + 2x+ 8 = 0
13. 5x3 + 4x2 + 4x− 1 = 0
14. x3 + 5x2 − 9x− 45 = 0
15. x3 + x2 − 6x = 0
16. 3x4 − 10x3 + 10x− 3 = 0
17. 2x4 + 5x3 − 5x− 2 = 0
18. x4 − x2 − 12 = 0
19. x4 − 13x2 + 36 = 0
20. x6 − 9x3 + 8 = 0
21. 3x3 − 15x2 − 6x+ 72 = 0
22. 4x3 + 13x2 − 13x− 4 = 0
23. 12x3 + 13x2 − 13x− 12 = 0
6
24. 2x4 − 5x3 + 4x2 − 5x+ 2 = 0
25. x4 + x3 − x− 1 = 0
26. x3 + 3x2 + 3x+ 1 = 0
27. 4x3 − 21x2 + 21x− 4 = 0
28. 6x3 − 7x2 − 7x+ 6 = 0
29. 3x3 − 2x2 − 2x+ 3 = 0
30. 2x4 − 3x3 + 3x− 2 = 0
31. 3x3 − (4√2− 3)x2 − (4
√2− 3)x+ 3 = 0
32. 5x3 + 4x2 + 4x− 1 = 0
33. x4 − 3x3 + x2 − 2x− 3 = 0
34. x4
3− x3
2+ x2 − x+ 1
6= 0
35. 2x4 − 7x3 + 3x2 + 8x− 4 = 0
36. x3 + 5x2 − 9x− 45 = 0
37. 8x3 − 18x2 + x+ 6 = 0
38. 2x4 − 11x3 − 6x2 − 7x = 0
39. x4 − 6x3 + 13x2 − 12x+ 4 = 0
40. 4x4 − 5x2 + 1 = 0
7
Equazioni irrazionali
1.√2x− 1 = 2
2.√2x+ 3 = 3
3.√3x+ 1 = 2
4.√x+ 2 = 6
5.√10− 3x = −5
6.√3− x = 4
7.√x+ 1 = 10
8. 3 +√4− x = 0
9.√x+ 1 = 1
10.√x− 1 = 3
11.√28− x− x2 = 4
12.√x2 + 1 = 4
13.√x2 − 9x+ 23− 3 = 0
14.√4x− 7 = x− 3
15.√8− x = 2x− 6
16.√x+ 2 = x+ 2
17.√5 + 2x− 5 = 2x
18.√2x− 5 + 2 = x
19.√x+ 5 + 6 = x+ 5
20.√3x2 + 5x− 3 = x
21.√2x2 − 3x− 10− x = 0
22.√5− 3x =
√5x− 35
23.√3x+ 7 =
√4x+ 5
8
24.√8− 7x =
√6x2 + 5
25.√x2 + 3x− 3 =
√x
26.√3x2 + 3x− 1 =
√x
27.√x+ 2 +
√1− 3x = 0
28.√x+ 1 +
√3x+ 1 = 0
29.√x+ 1−
√x− 1 = 1
30.√4− 2x−
√2x− 3 = 1
31.√x− 9−
√x− 18 = 1
32.√6− 2x+
√4x− 3 = 3
33.√x+ 4 +
√x− 8 = 6
34.√4− x+
√x− 3 = 1
35.√5− x+
√x− 3 = 2
36.√x− 1 + 2 = 6−
√x− 7
37.√x2 + 3x− 3 =
√x
38.√6x2 − 2x− 1 =
√1− x
39.√14x2 − 2x− 1 =
√3x
40.√x2 + 2x− 14 =
√x− 2
9
Equazioni esponenziali
1. 3x = 27
2. 2x = 116
3. 2x+1 = 8
4. (3x+1)2 = 9
5. 25x−2 = 18
6. 32x+1
9= 3x−2
7. x−1√9 = 3x−1
√3
8. 2x−3 · 4x+1 = 4
9. 23x = 82x+2
10. 8x2+2x = 1
8
11. 43x2−5x+1 = 1
4
12. (2x−1)x+1 = 8
13. (81+x)x = 1
14.3√32x−1 · x
√9 = 3x
15. x+1√8x · 2x
√22−x =
x√2x+2
16. (52−x)3+x
25x−1 = (5x−2)2x−3
252x·1253
17.x+2√28 · x−1
√8 =
2x−1√83 · x−1
√4
18. 2x−1 · 3 = 51+x
19. 5 · 2x+3 = 320 · 3x−3
20. 3x−2 · 7x−2 = 4x+3
21. 2x + 2x−1 + 2x−2 + 2x−3 + 2x−4 = 62
22. 3x + 3x−3 − 3x−4 + 3x−5 = 250
23. 22x+1 − 6 = 4x − 22x−1
10
24. 3x+1 + 3x−1 = 4x + 22x−1
25. 2 · 3x+1 − 3 · 5x+1 = 6 · 5x − 3x+2
26. 7x+1 − 52+x = 7x−1 − 51+x
27. 32x+1 − 52x−1 = 25x − 9x−1
28. 432−x − 4 · 51+x = 2 · 5x − 6
31−x
29. 2 · 3x−1 + 5 · 3x+1 = 23x+2 − 23x−1
30. 4x+2 − 5x−1 = 5x+1 − 22x−1
11
Equazioni logaritmiche
1. log(x− 1) = log(4− 3x)
2. log(3x+ 2) = 3 log 2
3. log(x− 2) + log(2x− 3) = log 3
4. 13log(x2 + 7) = log(x+ 1)
5. 12log(2x− 3) = log 5
6. 2 log x+ log 3 = log(5x− 2)
7. log(x−√1− x2) = 0
8. log x = 2 log(x− 2)
9. log(x+ 2) + log(3x+ 1) = 3 log 4
10. log(x+ 2)− 2 log 3 = log 6− log(x− 1)
11. 12log x+ log 3 = 1
2log 4 + log(x− 1)
12. 2 log x− log(x+ 1) = log 9− 2 log 2
13. log x+ log(2x− 1)− log 3 = log(2x+ 5)
14. log(3x+ 1) + log 3 = 4 log 2 + log(x− 2)
15. 3 log 2 + log(x− 1) = 2 log(x+ 1)
16. log(2− x) + log(x+ 1) = log 2
17. 12log x+ 1
2log(x− 1) = log 2 + 1
2log 5
18. 1 + log(x− 1) = log 5
19. 1 + log√x− 2 = log 5 + 1
2log(2x− 1)
20. 12log(12x+ 16) = log(x+ 3)
21. 12log(3x+ 4) = log(x+ 3)− log 2
22. log(3x+ 1) + log(x+ 1) = log 2 + log(9x2 − 1)
23. 2 + log x = 12log(x+ 2)− log 0.01
12
24. log(x− 1) + log√2 = 1
2log(x2 + 7)
25. log2(x2 + 2)− 2 log2 x = log2 3− log2(x
2 − 2)
26. logx(2x+ 3) = 2
27. logx2+2(x+ 1) = 12
28. log3(√x− 1− 2) = 1
29. log2(3x− 2) = 1 + 12log2(5x
2 − 14x+ 1)
30. 2 log3(x+ 2) + log3(x− 1)2 = 2 log3(5x− 2)
13
Equazioni trigonometriche
1. cos(x) =√32
2. sin(x) = 0
3. sin(x) = 1
4. sin(x) = 12
5. sin(x) = −12
6. 2 sin(x) = 3
7. 3 cos(x) = −5
8. cos(x) = −√22
9. 5 sin(x) = 6
10. tan(x) =√3
11. cot(x) = −√3
12. sin(x) = −√22
13. cos(x) = −12
14. sin(x)−√32
= 0
15. tan(x) = 1
16. 2 cos2(x)− 1 = 0
17. 5− 2 sin2(x) = 0
18.√2 sin2(x)− sin(x) = 0
19. cos(x)(sin(x)−
√22
)= 0
20. 4 sin2(x)− 1 = 0
21. −2cos2(x) + 1 = 0
22. sin(2x) = 12tan(x)
23. sin(2x) + 2 cos2(π4− x) = 3
14
24. cos(2x) + sin2(x) = 12
25. cos(2x) = cos(x)
26. sin(x) cos(x) = 32
27. sin(x) cos(x) = 1
28. cos(2x) = 1− sin2(x)
29. sin(x) = cos(2x)
30. cos(x) = 2 sin2(x)− 1
31. 3 sin2(x) + 2 cos(x) = 2
32. 2− sin(x) = cos2(x) + 7 sin2(x)
33. cos(2x) + 2 sin2(x) = 1
34. cos(2x)− 2 sin2(x) = 1
35. 2 sin(2x) + 2 sin2(x) = 3
36. sin(2x) + sin2(x) = 1
37. sin4(x)− sin2(x) cos2(x)− 2 cos4(x) = 0
38. 3 sin(x) +√3 sin(x) = −
√3
39. cos2(x) + 2 = 3 cos(x)
40. cos(2x) + 1 = 2 cos(x)
15
Disequazioni razionali intere di primo grado
1. 12x− 1 < 1 + 2(x+ 4)
2. 3 + 4(1 + x)− (1 + 3x) > −2
3. 3(x− 1)− 2 < 5x+ 1
4. 4(2x− 1)− 3(1− 2x) > 5
5. x3− (x−4)
2> 5−x
6+ 1
6. 3 + 2(x− 1) > 7 + 5(x− 2)
7. 8(5− x) + 3(x− 5) > 0
8. 9(20− 5x) + 27 > 8(5x− 6)
9. x−13− 1
2< 2(x+ 1) + 1
3
10. 1+3x3− (x−1)
4< x+6
6− 1
3
11. 2+3x4− x−2
3> 1
12. 12x+ x+3
3− x
4< 8
13. 12[2x− (1 + x)] > x− 1
3(1− 3x)
14. 13
(x− 1
2
)− 1
2
(x− 1
3
)< x−4
2
15. 1−x4− 2x−1
2> 3x−1
4− 5
(x+ 1
3
)16. 2
3
[3(x− 2) + 1−2x
4− x
2
]< x+ 1
2
17. 12− 1
3[x− 2(1− 3x)] < x−1
6− x+1
5
18. 4[x−23− 2
(x−16− 1−x
9
)]< x− 8
19.2− 1
3x
5− 1− 2
3x
4< 2−
12−3x10
20. 2−x1+ 1
2
− 3−x2− 1
2
> 2(1+6x)3
16
Disequazioni razionali intere di secondo grado
1. x(9− 2x) ≤ 0
2. x(x− 4) < 0
3. (2x+ 5)(x− 1) < 0
4. (x+ 4)(2x+ 5) > 0
5. 12x2 − 4x+ 3 < 0
6. −5 + 4x− 3x2 < 0
7. x2 − 5x+ 4 > 0
8. 2x2 − 7x− 15 ≥ 0
9. x2 + 4x < 0
10. 12x2 − 17x− 105 < 0
11. x2 + 6x+ 9 ≤ 0
12. x2 − 14x+ 49 < 0
13. 3x2 − 5x+ 9 > 0
14. 2x2 − 9 > 0
15. 9x2 − 25 < 0
16. x2 − 4x < 0
17. x2 − 10x+ 25 > 0
18. x2 − 81 ≥ 0
19. 25− x2 ≤ 0
20. x(x− 4) ≤ 0
21. (x− 2)(x− 3) > 0
22. (2x− 1)(x+ 1) > 0
23. (1− x)(x+ 1) > 0
17
24. (x− 2)(2 + x) < 0
25. x2 − 9 > 0
26. 4x2 − 1 < 0
27. 1− 25x2 < 0
28. 9− 49x2 > 0
29. (5 + 2x)(3 + x) < 0
30. (4− x)(1 + 2x) < 0
31. (3x+ 1)(1− x) > 0
32. x(x+ 5)− 7(x+ 8) < 7
33. 2− 2(2x− 1) + 4x2 − 3 > 0
34. (x− 2)2 − 4(x− 3) > 0
35. 2x2 − 4(x− 3)− 2x+ 7(4x− 1) < (x+ 1)2
36. x2+4−4x3− x−5
2< 5−3x
2+ x−3
2
37. 3−2x2− (x−1)2
4< 3
38. x2+164− x−3
2< 1− x
39. x2
4− (x+ 4)(x− 5) > (2x+1)
2
40. (x+1)2−(x−3)23
> (x+2)2
2− x
18
Disequazioni razionali intere di grado superiore al secondo
1. x(x4 − 7x2 + 12) > 0
2. x3 − 3x2 + 3x− 2 > 0
3. x3 + x > x2 + 1
4. x3 − 4x2 + 3x > 0
5. (5− 2x)(x2 − 7x+ 12) < 0
6. x3 − 12x2 + 32x > 0
7. 3x3 + 2x > 5x2
8. x3
2− 11x2
2+ 5x < 0
9. x3 − x2 + 4x < 0
10. 2x3 > x+ 1
11. x3 − x2 − 4x+ 4 > 0
12. 4x3 − 9x2 + 9x− 4 < 0
13. x4 − 5x2 + 4 > 0
14. x4 − 16 < 0
15. x3 + x2 − 10x+ 8 > 0
16. 2x3 − x2 − 2x+ 1 < 0
17. 4x3 − 12x2 + 5x+ 6 > 0
18. x3 − 4x2 − 19x− 14 > 0
19. x4 − 2x3 − x2 + 2x < 0
20. 3x4 − 2x3 + 2x2 − 2x− 1 > 0
19
Disequazioni razionali fratte
1. x+ 6x< 7
2. 1x2
+ 3x≤ 11
3. x−46−5x−x2 > 0
4. (x+3)(x+2)x2−2x+1
≤ 0
5. 1x2−5x+6
> 0
6. − 3(x−3)2 < 0
7. 4x2−9 > 0
8. 2x−x22x2−3x+7
≥ 0
9. 6x2+7x−31−4x2 ≥ 0
10. x2−5x+6x2−8x+15
< 0
11.3x2−6x+ 5
3
x2+6x− 455
≤ 0
12. 2x−1x2+3x−4 < 0
13. 4x2−5x−62x+1
< 0
14. 4x2+4x+12x−7 < 0
15. 18−3x−x2x+6
> 0
16. 3x2−7x+2x−1 < 0
17. (7x2−28)(x+2)x+5
< 0
18. (x−1)(x−2)x2−x−4 > 1
19. 2x2−6x+32x2−6x+3x2−5x+4
> 1
20. x2−5x+4x2+5x+4
> 0
21. x−5x+3
< x−8x−3
22. 4x+3
> 4x−3 −
13
23. 13x+4≤ 15
2x−3
20
24. 62x−1 > 5
x−2
25. x+1x−1 ≥
x−2x+2
+ 95
26. x+7x+1
< 15x2−1 −
xx−1
27. x2−3x+2x2+3x+2
> 0
28. 4x2+3x−13x2−4 ≤ 0
29. 3x2+5x+22x2−x+2
≤ 0
30. 2x2−3x+1x2−7x+6
> 0
31. 2x−1x−3 ≤
x+1x−1
32. 7x−4x2−4 −
2x−2 < 7
x+2
33. x3+x2
3+ x2
x+3< x3 − x2
3x+9
34. x3−x22−3x+2
> 0
35. x2−4x+1−x2+12x−3 > 0
36. x2−3x−4x2
< 0
37. 3x+23
< x−72x+1
38. x2+10x+16x−1 > 0
39. 2x2−6x+3x2−5x+4
> 1
40. x2−5x+4x2+5x+4
> 0
21
Disequazioni irrazionali
1.√x− 3 > 3
4
2.√x− 1 < 1
4
3.√x <√2x− 1
4.√x− 1 <
√2x− 3
5.√x− 2 <
√x− 1
6.√2x− 1 >
√3x− 4
7.√x− 1 ≥
√x
8.√x2 + 4x− 5 >
√x2 + 4x− 21
9. x− 5 >√x2 − 81
10.√x+ 7 > 13− x
11.√x2 − 1 > x+ 5
12.√x2 − 1 < x+ 5
13. 6x− 8 >√x2 − 5x+ 6
14. 2x− 1 >√x2 − 3x+ 2
15. 2x− 3 >√x2 − 5x+ 4
16. 3x− 2 >√x2 + x+ 1
17. 2x+ 3 >√x2 − 5x+ 6
18. x− 2 <√x2 + 4
19. x− 2 >√x2 + 4
20. 1− x <√x2 − x
21.√x2 + 3x− 1 > x+ 2
22. x− 1 <√x2 + 2x+ 4
23. x− 1 >√x2 + 2x+ 4
22
24. 2x+ 1 <√4x2 − 4x− 15
25. 4(x− 1) <√
(x+ 5)(3x+ 4)
26. 2x− 1 > 3√8x3 − 20x+ 11
27. x+√x2 − 5 < 5
28. 2(2x+ 1) + 3√−x2 − x+ 6 > 0
29.√2x+ 1 +
√x+ 1 < 1
30.√x+ 6 >
√x+ 1 +
√2x− 5
31.√2x+ 3 +
√5− 8x
32. 6x+ 3 <√−x2 − x+ 6 <
√4x+ 7
33.√x+√x− 1 >
√x+ 1
34.√2x− 3 +
√3x− 2 >
√x+ 10
35. 8x− 3 >√x2 − 15x+ 54
36. x−√25− x2 > 7
37.√2x2 − 5x+ 2 > 3x2 − x− 1
38. x4 − 1 >√−2x− x4
39. 2x− 1 <√1− x2
40.√2x− 1 <
√1− x2
23
Disequazioni logaritmiche
1. 2 log x < 1
2. log(x2 − 1) < 0
3. log(x2 − x− 1) > 0
4. log(6x− 8− x2) > 0
5. log(2x2 − 5x+ 3) < 0
6. log(x− 3) > 1
7. log5(x− 7) > 2
8. log1/2 x > 2
9. log3 x > 12
10. log1/2(3x− 2) > 3
11. log1/3(x2 − 3) > 0
12. log2(x2 − 3
4
)< −2
13. log2x+3x
> 1
14. log2 x+ log2(4− x) < log2 3
15. 4 log2(2x− 1) < 3
16. log x+ log(x− 2) < 0
17. log1/2 x+ log1/2(x− 1) > 0
18. log2(x2 + x+ 1) > log2 7− log2(x− 1)
19. log2 x+ 3 log x+ 2 < 0
20. 2 log2 x− 5 log x > 7
24
Disequazioni esponenziali
1. 5x > 25
2.(13
)x< 0
3.(12
)x>(12
)2(x−2)4. 4x − 3 · 2x + 2 < 0
5. 2(12
)x − 2x < 1
6.(12
)x+9> 4
7. 2x+2 + 2x − 20 > 0
8. 1
2x2< 1
4
9. 9 ∗ 3x > 19
10. 52x − 6 ∗ 5x + 5 > 0
11. 22x − 5 ∗ 2x + 4 < 0
12. 32x−4 − 4 ∗ 3x−2 + 3 > 0
13. 42x+1 − 16x−1 > 73· 9x + 7 · 32x
14. 4x − 10 · 2x + 16 > 0
15.(15
)x − 35> 2
51−x
16. 9x + 2 · 3x+1 − 27 > 0
17. (2x−1 − 1)(32x+1 − 9) > 0
18. 3− 21−x −(14
)x> 0
19. 3x−122x+2x−2 > 0
20. 3x+1−3x−1
2·3x+32x+1> 1
2
25
Disequazioni trigonometriche
1. cos(x) >√32
2. sin(x) < 0
3. cos(x) < 0
4. sin(x) ≤ 1
5. sin(x) > 12
6. sin(x) > −12
7. 2 sin(x) ≥ 3
8. 3 cos(x) ≤ −5
9. cos(x) ≤ −√22
10. 5 sin(x) < 6
11. tan(x) >√3
12. cot(x) < −√3
13. sin(x) ≤ −√22
14. cos(x) ≥ −12
15. sin(x)−√32
< 0
16. tan(x) ≥ 1
17. 2 cos2(x)− 1 < 0
18. 5− 2 sin2(x) < 0
19.√2 sin2(x)− sin(x) ≥ 0
20. cos(x)(sin(x)−
√22
)≤ 0
21. 4 sin2(x)− 1 ≤ 0
22. −2cos2(x) + 1 < 0
23. 2 sin2(x)− sin(x) < 0
26
24. 2 sin2(x) > 3 sin(x)− 1
25. 2 cos2(x)− 3 cos(x) < −1
26. 2 sin(x)− sin(2x) > 0
27. 3 sin(x) +√3 sin(x) < −
√3
28. cos2(x) + 2 < 3 cos(x)
29. cos(2x) + 1 > 2 cos(x)
30. cos(x)2 sin(x)−1 > 0
31. 1−√2 sin(x)√
2 cos(x)+1> 0
32.sin(2x)+ 1
2
cos(x)≤ 0
33. sin2(x)−3 sin(x)+2sin(x)
> 0
34. cos2(x) + 2 sin(x) cos(x)− sin2(x) < 0
35. 3 sin(x)−√3 cos(x) ≥ 0
36. sin(x) ≥ cos2(x)
37.√3 sin(x) cos(x) > − cos2(x)
38. 2 sin(x)+1cos(x)
< 0
39. cos(2x) + cos(x) ≤ 0
40. 5− 2 cos2(x) < 0
27
Sistemi di disequazioni
1. x2 − 3x+ 2 > 0
2x− 6 < 0
2. 15 > x+ 2x2
17x > 6x2 + 5
3. x2 − 2x− 3 > 0
x2 − 11x+ 28 ≥ 0
4. x2 − 1/4 > 0
−2x2 + 5x− 3 > 0
5. 3x2 − 4x+ 1 > 0
3x2 − 5x+ 2 ≤ 0
6. x(3− x) ≥ 0
(−x− 2)(1− x) ≥ 0
7. x(x− 4) + (3x+1)4≥ 3(1+x)
4− 3
4
3x2 + 7x+ 2 > 0
8. x(x− 14) < x2 − 1
36+ x
3+ 1
12
3x+ 2 > 4x(x− 1)
28
9. 3(4x+ 1)(4x− 1) > 6− x2
3(x2 − 2) < 43
10. (3x+ 1)2 ≤ x(x− 53+ 1 + 2x
3
(3x− 2)x+ x− 43< 2
3− 2x
11. {2x ≥ 2 (x−2)
3+ x− 1 + (x−1)
23(x+ 1
3)2 > (x− 1
9)(x− 3)
12. 7x(x+ 2)− 2 > x+ 4(5x2 − 3x) + 5(5x− 3)
2(x+ 6) ≤ 2x(2x+ 1)− x2
13. x(x− 2) + 5x2> 6(x− 1)− x
2
(x+1)2
3+ (x2−1)
2− 3x ≤ 3(x+1)2
2− (2x2−11)
3
14. (x− 12)2 + (x−3)2
4− 33 > (3−10x)
4
x(x− 12) < 1
2
15. −3(4x−1)
2≥ (3x− 1)2 − 7
4
2x2 − x2> x2 − 2
5(x− 1
10)− x
10
16. (x+1)
5> −2− x2
2
(x−2)7
< 3 + (x2−1)2
17. x2 − 5x+ 6 > 0
2x > x+ 1
3x− 2(x+ 1) < 2
29
18. 4(x− 1)2 < (2x+ 3)2 − (1−x)
3
(2−x)2− 1
5> (x−5)
3
(x− 2)(x+ 2) < (x− 23)(x+ 1
3)
19. x2 − x− 2 > 0
x2 + 3 > x(x+ 1)
x < 2(x+ 1)
20. (2x+1)
5− (2−x)
3> 1
x2 − 6x− 7 < 0
x2 − 8x+ 15 > 0
21. (x+2)
4+ x
3< (x−4)
2+ 3
(5x−2)3
+ 1 > (2x−3)2
x2 − 2x− 3 > 0
22. 2x(x+ 5) > 3(x+ 1)2
x2 + 4x+ 3 > 3(x− 1)2
x2 − 16 < (2x− 7)2
23. 2x+15− 2−x
3> 1
x2 − 6x− 7 < 0
x2 − 8x+ 15 > 0
30
24. 2x(x+ 5) > 3(x+ 1)2
x2 + 4x+ 3 > 3(x− 1)2
x2 − 16 < (2x− 7)2
25. (x− 1)2 < (2x+ 1)(x+ 1)
12x2 + x− 1 > 0
x2 + 6x < 6 + x8+ (x+2)(2x−3)
4
26. 2x2 > 3(9− x)
x(x−5)5
< 5x+ 645
(x+ 4)(2x+ 5) > 0
27. 2(5x2 − 9) < 6x2 + 63
3x− 2 ≤ 5− x2
28. x2 − 14> 0
−2x2 + x− 3 > 0
29. 3x2 − 2x+ 7 < 0
2x(2x− 13) > 7x
4+ 5
30. x2
2+ x+1
5> −2
x−27− x2−1
2< 3
31