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

Absolute Value (of x) Symbol lxl The distance x is from 0 on the number line. Always positive Ex: l-3l=

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--_

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

Insert or= sign in the shaded area to make the statements true 1. |6| …… |-6| 2. |2|…….|-3| 3. |9|….....-| |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|=… ……0 4)|-12|=… ……-4 5)|0|=… 15. ½…..-2/3 6)|54|=… 16. 3/5…..4/5 7)-|-8|=… ….0.4 8)-|92|=… … )-|65|=… /2……-1 10)-|-34|=… 20. 0….-0.9

21. 4… /4…… … …… /9….-5/ …… /2…..3/ … … …… …… … … ½…..-1/ …… /3….3/ /3… /2…..7/ /2….-3/ ….-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|….|-4| 46. |-1.9|… …… |-9/2| ……|5| 49. |-6/2|…….|-2/6|

Insert either or = sign in the shaded area to make a statements True /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/ /3………2/ /8-1/2……..5/2+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.