Solution - Absolute value equations

Absolute Value Equation entered :

      |x+4/5|=6/7 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |x+(4/5)| = (6/7) 

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 |x+(4/5)|

 For the Negative case we'll use -(x+(4/5)) 

For the Positive case we'll use (x+(4/5)) 

Step  3  :

Solve the Negative Case

      -(x+(4/5)) = (6/7) 

     Multiply
      -x-(4/5) = (6/7) 

     Rearrange and Add up
      -x = (58/35) 

     Multiply both sides by (-1)
      x = -(58/35) 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (x+(4/5)) = (6/7) 

     Rearrange and Add up
      x = (2/35) 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=-58/35
 x=2/35

Solutions on the Number Line

Two solutions were found :

1.  x=2/35
   
2.  x=-58/35