Solution - Absolute value equations

Absolute Value Equation entered :

      256=4+7|f| 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      256 = 7|f|+4 

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

      7|f| = 252 

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 7|f|

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

For the Positive case we'll use 7(f) 

Step  3  :

Solve the Negative Case

      -7(f) = 252 

     Multiply
      -7f = 252 

     Divide both sides by 7
      -f = 36 

     Multiply both sides by (-1)
      f = -36 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      7(f) = 252 

     Multiply
      7f = 252 

     Divide both sides by 7
      f = 36 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 f=-36
 f=36

Solutions on the Number Line

Two solutions were found :

1.  f=36
   
2.  f=-36