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Mathematics LibreTexts

4.10E: Exercises

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Solve Rational Inequalities

In the following exercises, solve each rational inequality and write the solution in interval notation.

1. x3x+40

Answer

(,4)[3,)

2. x+6x50

3. x+1x30

Answer

[1,3)

4. x4x+20

5. x7x1>0

Answer

(,1)(7,)

6. x+8x+3>0

7. x6x+5<0

Answer

(5,6)

8. x+5x2<0

9. 3xx5<1

Answer

(52,5)

10. 5xx2<1

11. 6xx6>2

Answer

(,3)(6,)

12. 3xx4>2

13. 2x+3x61

Answer

[9,6)

14. 4x1x41

15. 3x2x42

Answer

(,6](4,)

16. 4x3x32

17. 1a+25=12

Answer

a=10

18. 1x24x12>0

19. 3x25x+4<0

Answer

(1,4)

20. 4x2+7x+12<0

21. 22x2+x150

Answer

(,3)(52,)

22. 63x22x50

23. 26x213x+60

Answer

(,23)(32,)

24. 110x2+11x60

17. 1a+25=12

Answer

a=10

18. 1x24x12>0

19. 3x25x+4<0

Answer

(1,4)

20. 4x2+7x+12<0

25. 12+12x2>5x

Answer

(,0)(0,4)(6,)

26. 13+1x2>43x

27. 124x21x

Answer

[2,0)(0,4]

28. 1232x21x

29. 1x216<0

Answer

(4,4)

30. 4x225>0

31. 4x23x+1

Answer

[10,1)(2,)

32. 5x14x+2

Solve an Inequality with Rational Functions

In the following exercises, solve each rational function inequality and write the solution in interval notation.

33. Given the function R(x)=x5x2, find the values of x that make the function less than or equal to 0.

Answer

(2,5]

34. Given the function R(x)=x+1x+3, find the values of x that make the function less than or equal to 0.

35. Given the function R(x)=x6x+2, find the values of x that make the function less than or equal to 0.

Answer

(,2)[6,)

36. Given the function R(x)=x+1x4, find the values of x that make the function less than or equal to 0.

Writing Exercises

37. Write the steps you would use to explain solving rational inequalities to your little brother.

Answer

Answers will vary

38. Create a rational inequality whose solution is (,2][4,).


This page titled 4.10E: Exercises is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax.

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