Solution - Absolute value equations

Absolute Value Equation entered :

      |6x-3|=27 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |6x-3| = 27 

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 |6x-3|

 For the Negative case we'll use -(6x-3) 

For the Positive case we'll use (6x-3) 

Step  3  :

Solve the Negative Case

      -(6x-3) = 27 

     Multiply
      -6x+3 = 27 

     Rearrange and Add up
      -6x = 24 

     Divide both sides by 6
      -x = 4 

     Multiply both sides by (-1)
      x = -4 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (6x-3) = 27 

     Rearrange and Add up
      6x = 30 

     Divide both sides by 6
      x = 5 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=-4
 x=5

Solutions on the Number Line

Two solutions were found :

1.  x=5
   
2.  x=-4