Equações Modulares

1- Resolva :

a)|5-3X| = 4

        x-1
b)| ______  | = 2
 
         3


      2X+1
c)|______ = 5/6

        4


 d) |4+3X| = 1




       X+2
e)|______| = 5 |X /=2)

        X-2

Gabaritos:

• a) Caso 1

5-3X = 4
-3X = 4-5
-3X = -1
X = 1/3

• Caso 2

5-3X = -4
-3X = -4-5
-3X = -9
X = 9/3 = 3

S = {1/3, 3}

• b) Caso 1 

   X-1
|_____| = 2
     3


X-1 = 6
X = 6+1
X = 7

• Caso 2

     X-1
|______| = -2
     3




X-1 = -6
X = -6+1
X = -5

S = {-5, 7}

•  c)Caso 1 

    2X+1

|_______| = 5/6

      4 

 12X + = 20

12X = 20-6

12X = 14

X = 14/12

X = 7/6

• Caso 2 

    X+1

|______| = -5/6 

      4

 12X+6 = -20

12X = -20-6

X = -26/6

X = -13/6

S = {-13/6, 7/6}

• d) Caso 1 

|4+3X| = 1

4+3X - 1

3X = 1 - 4

3X = -3

X-1

• Caso 2 

|4+3X| = -1

4+3X = -1

3X = -1-4

3X = -5

X = -5/3

S = {-5/3, -1}


     

• e) Caso 1

     X+2
 _______ = 5/1
      X-2




X+2 = 5X-10
-5X+X = -10-2
-4X = -12
X = 12/4
X = 3

• Caso 2 

  X+2
_____ = -5/1
  X-2


X+2 = -5X+10
6X = 8-2
X = 8/6
X = 4/3


S = {3, 4/3}