Solution - Absolute value inequalities

Absolute Value Inequality entered :

      3|x-8|+4>19 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered
      3|x-8|+4 > 19 

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

      3|x-8| > 15 

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 3|x-8|

 For the Negative case we'll use -3(x-8) 

For the Positive case we'll use 3(x-8) 

Step  3  :

Solve the Negative Case

      -3(x-8) > 15 

     Multiply
      -3x+24 > 15 

     Rearrange and Add up
      -3x > -9 

     Divide both sides by 3
      -x > -3 

     Multiply both sides by (-1)
     Remember to flip the inequality sign
      x < 3 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      3(x-8) > 15 

     Multiply
      3x-24 > 15 

     Rearrange and Add up
      3x > 39 

     Divide both sides by 3
      x > 13 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

  x < 3
  x > 13

Solutions in Interval Notation

    (-∞,3)
 
    (13,+∞) 

Solutions on the Number Line

Two solutions were found :

1.   x > 13
2.   x < 3