Solving Absolute Value Solving Absolute Value Equations & InequalitiesEquations & Inequalities

Zafar-iqbal

Absolute Value (of x)

• Symbol lxl

• The distance x is from 0 on the number line.

• Always positive

• Ex: l-3l=3

-4 -3 -2 -1 0 1 2

Ex: x = 5

• What are the possible values of x?

x = 5 or x = -5

Absolute is the distance from zero to both side on number line

means left right

|-4| shows the direction of distance from zero to left side

while |4| shows the direction of

distance from zero to right side_4--_3--_2--_1--0--1--2--3--4--

That's why |4|=4and

|-4|=4In short words absolute value is

always positive.Absolute is distance so distance

will always positive

Insert < or >or= sign in the shaded area to make the

statements true1. |6| …… |-6|2. |2|…….|-3|3. |9|….....-|-94. -|10|…-|8|

5. -|-11|…...|-11|

Exercise 1.4 page #28

Evaluate Insert <,> sign to make

the statements true.

1)|4|=… 11. 2…….3

2)|-3|=… 12. 4……-2

3)|-15|=… 13. -3……0

4)|-12|=… 14. -6……-4

5)|0|=… 15. ½…..-2/3

6)|54|=… 16. 3/5…..4/5

7)-|-8|=… 17. 0.2….0.4

8)-|92|=… 18. -0.2….-0.4

9)-|65|=… 19. -1/2……-1

10)-|-34|=… 20. 0….-0.9

21. 4….-4 22. -3/4……..-1

23. -2.1…..-2 24.-1.83…….-1.82

25. 5/9….-5/9 26. -9……..-12

27. -3/2…..3/2 28. -4.09….-5.3

29. 0.49…..0.43 30. -1.0……-0.7

31. 5……..-7 32. 0.001….0.002

33.-0.006…-0.007 34. ½…..-1/2

35. -5…….-2 36. 5/3….3/5

37.-2/3….-3 38. 5/2…..7/2

39.-1/2….-3/2 40. -0.4….-0.5

Insert either <, > or = in the shaded area to make the statements true.

41.8….|-7| 50. |2/5|……|-0.40|

42. |-8|….|-7|

43. |0|……|2/3|

44. |-4|….-3

45. |-3|….|-4|

46. |-1.9|….-1.8

47. 4…… |-9/2|

48. -5……|5|

49. |-6/2|…….|-2/6|

Insert either <,> or = sign in the shaded area to make a statements True.

51. 2/3+ 2/3+ 2/3+ 2/3 ….4(2/3)

52. 2/3.2/3……..2/3+2/3

53. ½.1/2 …….1/2+1/2

54. 5+2/3………2/3+5

55. 5/8-1/2……..5/2+1/2

56.2.1/3.1/2……2.1/3+1/2

57.what number is 4 unit from zero on the number line.

58.what number is 5 unit from zero on the number line.

59.what number is 2 unit from zero on the number line.

60.Are there any number there absolute value is not positive? Explain your answer.

61.What is the absolute value of a number.