Solution - Absolute value equations

Absolute Value Equation entered :

      2|x-3|=x-1 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      2|x-3| = x-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 2|x-3|

 For the Negative case we'll use -2(x-3) 

For the Positive case we'll use 2(x-3) 

Step  3  :

Solve the Negative Case

      -2(x-3) = x-1 

     Multiply
      -2x+6 = x-1 

     Rearrange and Add up
      -3x = -7 

     Divide both sides by 3
      -x = -(7/3) 

     Multiply both sides by (-1)
      x = (7/3) 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      2(x-3) = x-1 

     Multiply
      2x-6 = x-1 

     Rearrange and Add up
      x = 5 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=7/3
 x=5

Solutions on the Number Line

Two solutions were found :

1.  x=5
   
2.  x=7/3