Solution - Absolute value equations

Absolute Value Equation entered :

      |1-2r|=7 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |-2r+1| = 7 

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 |-2r+1|

 For the Negative case we'll use -(-2r+1) 

For the Positive case we'll use (-2r+1) 

Step  3  :

Solve the Negative Case

      -(-2r+1) = 7 

     Multiply
      2r-1 = 7 

     Rearrange and Add up
      2r = 8 

     Divide both sides by 2
      r = 4 

Step  4  :

Solve the Positive Case

      (-2r+1) = 7 

     Rearrange and Add up
      -2r = 6 

     Divide both sides by 2
      -r = 3 

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

Step  5  :

Wrap up the solution

 r=4
 r=-3

Solutions on the Number Line

Two solutions were found :

1.  r=-3
   
2.  r=4