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Solving and Graphing Compound Inequalities with Step-by-Step Examples

This resource provides a clear guide on how to solve and graph compound inequalities. Using detailed examples, we explore the process of solving inequalities such as -5 < x - 4 < 2. The solution involves isolating the variable and transforming the inequality, followed by graphing the solution on a number line. Reinforce your understanding of compound inequalities with various practice problems and visual representations to help clarify the concepts. Perfect for students needing extra help or for educators seeking teaching aids.

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Solving and Graphing Compound Inequalities with Step-by-Step Examples

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  1. 5.4 – Solving Compound Inequalities

  2. Ex. Solve and graph the solution.

  3. Ex. Solve and graph the solution. a. -5 < x – 4 < 2

  4. Ex. Solve and graph the solution. a. -5 < x – 4 < 2

  5. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4

  6. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4

  7. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2

  8. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4

  9. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 -1 < x

  10. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x

  11. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6

  12. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6

  13. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x

  14. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x

  15. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x < 6

  16. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x < 6

  17. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x < 6

  18. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x < 6

  19. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x < 6

  20. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x < 6

  21. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x < 6

  22. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x < 6 0

  23. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x < 6 -1 0

  24. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x < 6 -1 0 6

  25. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 <x < 6 -1 0 6

  26. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 <x < 6 -1 0 6

  27. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x< 6 -1 0 6

  28. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x< 6 -1 0 6

  29. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x < 6 -1 0 6

  30. Ex. Solve and graph the solution. a. -5 < x – 4 < 2 -5 < x – 4 and x – 4 < 2 +4 +4 +4 +4 -1 < x and x < 6 -1 < x < 6 -1 0 6

  31. b. -3h + 4 < 19 or 7h – 3 > 18

  32. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4

  33. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 -3h < 15

  34. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 -3h < 15 -3 -3

  35. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 -3h < 15 -3 -3 h > -5

  36. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 -3 -3 h > -5

  37. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 h > -5

  38. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 7 7 h > -5

  39. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 7 7 h > -5 or h > 3

  40. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 7 7 h > -5 or h > 3

  41. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 7 7 h > -5 or h > 3 0

  42. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 7 7 h > -5 or h > 3 -5 0 3

  43. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 7 7 h> -5 or h > 3 -5 0 3

  44. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 7 7 h > -5 or h > 3 -5 0 3

  45. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 7 7 h > -5 or h> 3 -5 0 3

  46. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 7 7 h > -5 or h > 3 -5 0 3

  47. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 7 7 h> -5 or h > 3 -5 0 3

  48. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 7 7 h > -5 or h > 3 -5 0 3

  49. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 7 7 h > -5 or h> 3 -5 0 3

  50. b. -3h + 4 < 19 or 7h – 3 > 18 - 4 - 4 +3 +3 -3h < 15 or 7h > 21 -3 -3 7 7 h > -5 or h > 3 -5 0 3

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