4.10E: Exercises
( \newcommand{\kernel}{\mathrm{null}\,}\)
selected template will load here
This action is not available.
( \newcommand{\kernel}{\mathrm{null}\,}\)
In the following exercises, solve each rational inequality and write the solution in interval notation.
1. x−3x+4≥0
(−∞,−4)∪[3,∞)
2. x+6x−5≥0
3. x+1x−3≤0
[−1,3)
4. x−4x+2≤0
5. x−7x−1>0
(−∞,1)∪(7,∞)
6. x+8x+3>0
7. x−6x+5<0
(−5,6)
8. x+5x−2<0
9. 3xx−5<1
(−52,5)
10. 5xx−2<1
11. 6xx−6>2
(−∞,−3)∪(6,∞)
12. 3xx−4>2
13. 2x+3x−6≤1
[−9,6)
14. 4x−1x−4≤1
15. 3x−2x−4≥2
(−∞,−6]∪(4,∞)
16. 4x−3x−3≥2
17. 1a+25=12
a=10
18. 1x2−4x−12>0
19. 3x2−5x+4<0
(1,4)
20. 4x2+7x+12<0
21. 22x2+x−15≥0
(−∞,−3)∪(52,∞)
22. 63x2−2x−5≥0
23. −26x2−13x+6≤0
(−∞,23)∪(32,∞)
24. −110x2+11x−6≤0
17. 1a+25=12
a=10
18. 1x2−4x−12>0
19. 3x2−5x+4<0
(1,4)
20. 4x2+7x+12<0
25. 12+12x2>5x
(−∞,0)∪(0,4)∪(6,∞)
26. 13+1x2>43x
27. 12−4x2≤1x
[−2,0)∪(0,4]
28. 12−32x2≥1x
29. 1x2−16<0
(−4,4)
30. 4x2−25>0
31. 4x−2≥3x+1
[−10,−1)∪(2,∞)
32. 5x−1≤4x+2
In the following exercises, solve each rational function inequality and write the solution in interval notation.
33. Given the function R(x)=x−5x−2, find the values of x that make the function less than or equal to 0.
(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)=x−6x+2, find the values of x that make the function less than or equal to 0.
(−∞,−2)∪[6,∞)
36. Given the function R(x)=x+1x−4, find the values of x that make the function less than or equal to 0.
37. Write the steps you would use to explain solving rational inequalities to your little brother.
Answers will vary
38. Create a rational inequality whose solution is (−∞,−2]∪[4,∞).