1. Solving Absolute Value Equations & Inequalities Solving Absolute Value Equations & Inequalities Zafar-iqbal

2. 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

3. Ex: x = 5 What are the possible values of x? x = 5 or x = -5

4. Absolute is the distance from zero to both side on number line means left right

5. |-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--

6. That's why |4|=4 and |-4|=4 In short words absolute value is always positive. Absolute is distance so distance will always positive

7. Insert or= sign in the shaded area to make the statements true 1. |6| …… |-6| 2. |2|…….|-3| 3. |9|….....-|-9 4. -|10|…-|8| 5. -|-11|…...|-11|

8. 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

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

10. 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|

11. 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.