Inequações Modulares

1- Resolva:
a)|3X-1|>7

b)|2X+4|>12

c)|X-5 | ≥10

d)|5X-7|<2

e)|2X+2|<8

f)|X+2| ≤ 10


Gabaritos:
 Letra A

3X-1|>7< = >                                                                          

3X>7+1
3X>8
X>8/3 -->S
2,66


3X-1>7 ou 3X-1<-7

3X-1<-7
3X<-7+1
3X<-6
X<-2 --> S2

                                                        2,66
S1 ________________________,-------------------


                      -2
S2  ---------------,__________________________


                         -2                             2,66
S1 US2 --------------,______________,----------------



S = {XER |X>8/3 ou X<-2}





Letra B


|2X+4|>12 < = >

2X+4>12
2X>12-4
2X>8
X>8/2
X>4



2X+4>12 ou 2X+4<-10

2X+4<-12
2X<-12-4
2X<-16
X<-16
X<-8


S = {XER|X<-8 ou X>4}




Letra C

|2X-5|≥10 < = >

X-5≥10
X≥10+5
X≥15


X-5_<-10
X_<-10+5
X_<-5


S = {XER|X ≥-5 ou X≥15}



Letra D


|5X-7|<2 < = >

-2<5X-7
5X<7-2
5X<5
X<1


5X-7<2
5X<2+7
5X<9
X<9/5
1,8

S = {XER|1<X<1,8}





Letra E

|2X+2|<8 < = >

-8<2X+2
2X<-8-2
2X<10X<-5




2X+2<8
2X<8-2
2X<10
X<5



S = {XER| -5<X<3}