Solution - Absolute value inequalities

Absolute Value Inequality entered :

      |-4x-5|>9 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered
      |-4x-5| > 9 

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 |-4x-5|

 For the Negative case we'll use -(-4x-5) 

For the Positive case we'll use (-4x-5) 

Step  3  :

Solve the Negative Case

      -(-4x-5) > 9 

     Multiply
      4x+5 > 9 

     Rearrange and Add up
      4x > 4 

     Divide both sides by 4
      x > 1 

Step  4  :

Solve the Positive Case

      (-4x-5) > 9 

     Rearrange and Add up
      -4x > 14 

     Divide both sides by 4
      -x > (7/2) 

     Multiply both sides by (-1)
     Remember to flip the inequality sign
      x < -(7/2) 
     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

  x < -7/2
  x > 1

Solutions in Interval Notation

    (-∞,-7/2)
 
    (1,+∞) 

Solutions on the Number Line

Two solutions were found :

1.   x > 1
2.   x < -7/2