Solution - Absolute value equations

Absolute Value Equation entered :

      |2x-3|-5=13 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |2x-3|-5 = 13 

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

      |2x-3| = 18 

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 |2x-3|

 For the Negative case we'll use -(2x-3) 

For the Positive case we'll use (2x-3) 

Step  3  :

Solve the Negative Case

      -(2x-3) = 18 

     Multiply
      -2x+3 = 18 

     Rearrange and Add up
      -2x = 15 

     Divide both sides by 2
      -x = (15/2) 

     Multiply both sides by (-1)
      x = -(15/2) 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (2x-3) = 18 

     Rearrange and Add up
      2x = 21 

     Divide both sides by 2
      x = (21/2) 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=-15/2
 x=21/2

Solutions on the Number Line

Two solutions were found :

1.  x=21/2
   
2.  x=-15/2