Solution - Absolute value equations

Absolute Value Equation entered :

      |11x-3|+2=11 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |11x-3|+2 = 11 

Another term is moved / added to the right hand side.

      |11x-3| = 9 

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 |11x-3|

 For the Negative case we'll use -(11x-3) 

For the Positive case we'll use (11x-3) 

Step  3  :

Solve the Negative Case

      -(11x-3) = 9 

     Multiply
      -11x+3 = 9 

     Rearrange and Add up
      -11x = 6 

     Divide both sides by 11
      -x = (6/11) 

     Multiply both sides by (-1)
      x = -(6/11) 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (11x-3) = 9 

     Rearrange and Add up
      11x = 12 

     Divide both sides by 11
      x = (12/11) 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=-6/11
 x=12/11

Solutions on the Number Line

Two solutions were found :

1.  x=12/11
   
2.  x=-6/11