Solution - Absolute value inequalities

Absolute Value Inequality entered :

      |x-3|>2 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered
      |x-3| > 2 

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-3|

 For the Negative case we'll use -(x-3) 

For the Positive case we'll use (x-3) 

Step  3  :

Solve the Negative Case

      -(x-3) > 2 

     Multiply
      -x+3 > 2 

     Rearrange and Add up
      -x > -1 

     Multiply both sides by (-1)
     Remember to flip the inequality sign
      x < 1 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (x-3) > 2 

     Rearrange and Add up
      x > 5 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

  x < 1
  x > 5

Solutions in Interval Notation

    (-∞,1)
 
    (5,+∞) 

Solutions on the Number Line

Two solutions were found :

1.   x > 5
2.   x < 1