Solution - Absolute value equations

Absolute Value Equation entered :

      2|x+8|-3=11 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      2|x+8|-3 = 11 

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

      2|x+8| = 14 

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+8|

 For the Negative case we'll use -2(x+8) 

For the Positive case we'll use 2(x+8) 

Step  3  :

Solve the Negative Case

      -2(x+8) = 14 

     Multiply
      -2x-16 = 14 

     Rearrange and Add up
      -2x = 30 

     Divide both sides by 2
      -x = 15 

     Multiply both sides by (-1)
      x = -15 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      2(x+8) = 14 

     Multiply
      2x+16 = 14 

     Rearrange and Add up
      2x = -2 

     Divide both sides by 2
      x = -1 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=-15
 x=-1

Solutions on the Number Line

Two solutions were found :

1.  x=-1
   
2.  x=-15