Valor Absoluto

Actividades de valor Absoluto

1.- |x| <1

X < 1 verif /x=0

(-∞, 1 ) 0 < 1

2.- |x-3/2| > 5 verif / x= -8

5 < x-3/2 < -5 [ -7 , 13 ] |-8 -3 /2| > 5

5(2) < 2(x-3/2) < -5(2) (-∞ , -7] u [13 , ∞) |-11/2 | > 5 ---]---o-----[----

10 < x-3 < -10 11/2 > 5

10+3 < x-3+3<-10+3 5.5 > 5

13 < x < -7

3.- |1-2x/3 | < 1 _________________________________________________________________________

-1 < 1- 2x/3 < 1

(3)-1 < 3(1-2x/3) < 1(3) Verif/ X= 0

-3 < 1-2x < 3 |1- 2(0)/3|<1

-3-1 < 1-1-2x < 3-1 |1-0/3|

-4 < -2x < 2 1/3 < 1

-4/-2 < - 2x/-2 < 2/-2 ----(-o---)---

2 > x > - 1 (-1 , 2)

4.-|x/2| > 3______________________________________________________________________

3 < x/2 < -3 verif / X= 7

(2)3 < 2(x/2)<-3(2) |-7/2| > 3

6 < x < -6 3.5 > 3 ----)---o---(----

(-∞,- 6)u(6, ∞)

5.-|x+2| < 5_____________________________________________________________________

-5 < x + 2 < 5 Verif / x= 0

-5 -2< x+2-2 <5-2 |0 + 2| < 5

-7 < x < 3 2 < 5

( -7, 3 ) ------(--o--)-----

6.- |3x + 1| > 4___________________________________________________________________

4 < 3x+1 < -4

4-1 < 3x+1-1 < -4-1 Verif / x=0 x=-2

3 < 3x < -5 |3(0)+1| > 4 |3(-2)+1| >4

3/3 < 3x/3 < -5/3 |1| > 4 |-6+1| >4

1 < x < -5/3 1 > 4 |-5|>4

(-∞ , -5/3)u(1, ∞) -------]---o----[------

7.-|2x+3/5|< 2___________________________________________________________________

-2 < 2x+3/5 < 2

-2(5)<5(2x+3/5) < 2 (5) Verif / X=0

-10 < 2x +3 < 10 |2(0) +3/5|<2

-10 – 3 < 2x+3-3 < 10 -3 3/5 < 2 --------(---0---)-------

-13/2 < 2x/2 < 7/2

-13/2 < x < 7/2

(-13/2 , 7/2)

8.-| 7-3x/2 | < 1___________________________________________________________________

9.-| x+2 |<1 ______________________________________________________________________

-1 < x +2 < 1 Verif/ X= -2

-1-2 < x+2-2 < 1-2 |-2+2| < 1

-3 < x < -1 0 < 1 ----(--)-o---------

(-3 , -1)

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