Solution - Absolute value equations

Absolute Value Equation entered :

      |3x-1|=6x 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |3x-1| = 6x 

Step  2  :

Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |3x-1|

 For the Negative case we'll use -(3x-1) 

For the Positive case we'll use (3x-1) 

Step  3  :

Solve the Negative Case

      -(3x-1) = 6x 

     Multiply
      -3x+1 = 6x 

     Rearrange and Add up
      -9x = -1 

     Divide both sides by 9
      -x = -(1/9) 

     Multiply both sides by (-1)
      x = (1/9) 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (3x-1) = 6x 

     Rearrange and Add up
      -3x = 1 

     Divide both sides by 3
      -x = (1/3) 

     Multiply both sides by (-1)
      x = -(1/3) 
     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=1/9
 x=-1/3

Solutions on the Number Line

Two solutions were found :

1.  x=-1/3
   
2.  x=1/9