Solution - Absolute value equations

Absolute Value Equation entered :

      |-6x-3|=12 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |-6x-3| = 12 

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) = 12 

     Multiply
      6x+3 = 12 

     Rearrange and Add up
      6x = 9 

     Divide both sides by 6
      x = (3/2) 

Step  4  :

Solve the Positive Case

      (-6x-3) = 12 

     Rearrange and Add up
      -6x = 15 

     Divide both sides by 6
      -x = (5/2) 

     Multiply both sides by (-1)
      x = -(5/2) 
     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=3/2
 x=-5/2

Solutions on the Number Line

Two solutions were found :

1.  x=-5/2
   
2.  x=3/2