Solution - Absolute value equations

Absolute Value Equation entered :

      |5x-7|-3=9 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |5x-7|-3 = 9 

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

      |5x-7| = 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 |5x-7|

 For the Negative case we'll use -(5x-7) 

For the Positive case we'll use (5x-7) 

Step  3  :

Solve the Negative Case

      -(5x-7) = 12 

     Multiply
      -5x+7 = 12 

     Rearrange and Add up
      -5x = 5 

     Divide both sides by 5
      -x = 1 

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

Step  4  :

Solve the Positive Case

      (5x-7) = 12 

     Rearrange and Add up
      5x = 19 

     Divide both sides by 5
      x = (19/5) 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=-1
 x=19/5

Solutions on the Number Line

Two solutions were found :

1.  x=19/5
   
2.  x=-1