Solution - Absolute value equations

Absolute Value Equation entered :

      |4x-6|=2 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |4x-6| = 2 

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 |4x-6|

 For the Negative case we'll use -(4x-6) 

For the Positive case we'll use (4x-6) 

Step  3  :

Solve the Negative Case

      -(4x-6) = 2 

     Multiply
      -4x+6 = 2 

     Rearrange and Add up
      -4x = -4 

     Divide both sides by 4
      -x = -1 

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

Step  4  :

Solve the Positive Case

      (4x-6) = 2 

     Rearrange and Add up
      4x = 8 

     Divide both sides by 4
      x = 2 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=1
 x=2

Solutions on the Number Line

Two solutions were found :

1.  x=2
   
2.  x=1