Solution - Absolute value equations

Absolute Value Equation entered :

      |x-2|+3=7 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |x-2|+3 = 7 

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

      |x-2| = 4 

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 |x-2|

 For the Negative case we'll use -(x-2) 

For the Positive case we'll use (x-2) 

Step  3  :

Solve the Negative Case

      -(x-2) = 4 

     Multiply
      -x+2 = 4 

     Rearrange and Add up
      -x = 2 

     Multiply both sides by (-1)
      x = -2 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (x-2) = 4 

     Rearrange and Add up
      x = 6 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=-2
 x=6

Solutions on the Number Line

Two solutions were found :

1.  x=6
   
2.  x=-2