EXERCISE SET 2.7
Practice Exercises
Solve each polynomial inequality in Exercises 1-42 and graph the solution set on a real number line. Express each solution set in interval notation.
1. (x - 4)(x + 2) > 0
2. (x + 3)(x - 5) > 0
3. (x - 7)(x + 3) ≤ 0
4. (x + 1)(x - 7) ≤ 0
5. x^2 - 5x + 4 > 0
6. x^2 - 4x + 3 < 0
7. x^2 + 5x + 4 > 0
8. x^2 + x - 6 > 0
9. x^2 - 6x + 9 < 0
10. x^2 - 2x + 1 > 0
11. 3x^2 + 10x - 8 ≤ 0
12. 9x^2 + 3x - 2 ≥ 0
13. 2x^2 + x < 15
14. 6x^2 + x > 1
15. 4x^2 + 7x < -3
16. 3x^2 + 16x < -5
17. 5x ≤ 2 - 3x^2
18. 4x^2 + 1 ≥ 4x
19. x^2 - 4x ≥ 0
20. x^2 + 2x < 0
21. 2x^2 + 3x > 0
22. 3x^2 - 5x ≤ 0
23. -x^2 + x ≥ 0
24. -x^2 + 2x ≥ 0
25. x^2 ≤ 4x - 2
26. x^2 ≤ 2x + 2
27. 9x^2 - 6x + 1 < 0
28. 4x^2 - 4x + 1 ≥ 0
29. (x - 1)(x - 2)(x - 3) ≥ 0
30. (x + 1)(x + 2)(x + 3) ≥ 0
31. x(3 - x)(x - 5) ≤ 0
32. x(4 - x)(x - 6) ≤ 0
33. (2 - x)^2(x - 7/2) < 0
34. (5 - x)^2(x - 13/2) < 0
35. x^3 + 2x^2 - x - 2 ≥ 0
36. x^3 + 2x^2 - 4x - 8 ≥ 0
37. x^3 - 3x^2 - 9x + 27 < 0
38. x^3 + 7x^2 - x - 7 < 0
39. x^3 + x^2 + 4x + 4 > 0
40. x^3 - x^2 + 9x - 9 > 0
41. x^3 ≥ 9x^2
42. x^3 ≤ 4x^2
Solve each rational inequality in Exercises 43-60 and graph the solution set on a real number line. Express each solution set in interval notation.