Solution - Absolute value equations

Absolute Value Equation entered :

      4n-15=|n| 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      4n-15 = |n| 

Absolute value term is moved to the left hand side.
Two terms are moved / added to the right hand side.
To make the absolute value term positive, both sides are multiplied by (-1).

      |n| = 4n-15 

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 |n|

 For the Negative case we'll use -(n) 

For the Positive case we'll use (n) 

Step  3  :

Solve the Negative Case

      -(n) = 4n-15 

     Multiply
      -n = 4n-15 

     Rearrange and Add up
      -5n = -15 

     Divide both sides by 5
      -n = -3 

     Multiply both sides by (-1)
      n = 3 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (n) = 4n-15 

     Rearrange and Add up
      -3n = -15 

     Divide both sides by 3
      -n = -5 

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

Step  5  :

Wrap up the solution

 n=3
 n=5

Solutions on the Number Line

Two solutions were found :

1.  n=5
   
2.  n=3