Solving Linear Inequalities in Interval Notation and Number Line, Study notes of Algebra

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Interval Notation:

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Additional Example 7:

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For each of the following inequalities: (a) Write the inequality algebraically. (b) Graph the inequality on the real number line. (c) Write the inequality in interval notation.

1. x is greater than 5. 2. x is less than 4. 3. x is less than or equal to 3. 4. x is greater than or equal to 7. 5. x is not equal to 2. 6. x is not equal to ^5. 7. x is less than 1. 8. x is greater than ^6. 9. x is greater than or equal to  4. 10. x is less than or equal to  2. 11. x is not equal to ^8. 12. x is not equal to 3. 13. x is not equal to 2 and x is not equal to 7. 14. x is not equal to  4 and x is not equal to 0. Write each of the following inequalities in interval notation. 15. x  3 16. x  5 17. x  2 18. x  7 19.^3 ^ x ^5 20.  7  x  2 21. x^ ^7 22. x  9

46. 8  4 x  6  5 x

49. ^3 (^4 ^5 x )^ ^2 (^7  x ) 50. ^4 (^3 ^2 x )( x ^20 ) 51. (^) 65 ^13 x  21 ( x ^5 )

• 37.  5 x 
• 38.  4 x 
• 39. 2 x  5 
• 40.^3 x ^4 
• 41. 8  3 x 
• 42. 10  x 
• 43. 4 x  11  7 x 
• 44. 5  9 x  3 x 
• 45.^10 x ^7 ^2 x 
• 47. 5  8 x  4 x 
• 48. x  10  8 x 
• 53.  10  3 x  2  52. 52  x  21   31 ^10  x 
• 54. ^9 ^2 x ^3 
• 55.  4  3  7 x 
• 56.  19  5  4 x 
• 57. 32  3 x 15 ^10 
• 58. 43  5  6 2 x 
• 59. (a) 5  x  Which of the following inequalities can never be true?
  • (b) 9  x 
  • (c) ^3  x 
• (d)  5  x 