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