Solution - Absolute value equations

Absolute Value Equation entered :

      |7x-1|=1 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |7x-1| = 1 

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 |7x-1|

 For the Negative case we'll use -(7x-1) 

For the Positive case we'll use (7x-1) 

Step  3  :

Solve the Negative Case

      -(7x-1) = 1 

     Multiply
      -7x+1 = 1 

     Rearrange and Add up
      -7x = 0 

     Divide both sides by 7
      -x = 0 

     Multiply both sides by (-1)
      x = 0 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (7x-1) = 1 

     Rearrange and Add up
      7x = 2 

     Divide both sides by 7
      x = (2/7) 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=0  x=2/7

Solutions on the Number Line

Two solutions were found :

1.  x=2/7
   
2.  x=0