Solution - Absolute value equations

Absolute Value Equation entered :

      |-n+10|=3 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |-n+10| = 3 

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+10|

 For the Negative case we'll use -(-n+10) 

For the Positive case we'll use (-n+10) 

Step  3  :

Solve the Negative Case

      -(-n+10) = 3 

     Multiply
      n-10 = 3 

     Rearrange and Add up
      n = 13 

Step  4  :

Solve the Positive Case

      (-n+10) = 3 

     Rearrange and Add up
      -n = -7 

     Multiply both sides by (-1)
      n = 7 
     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 n=13
 n=7

Solutions on the Number Line

Two solutions were found :

1.  n=7
   
2.  n=13