Solution - Absolute value inequalities

Absolute Value Inequality entered :

      |7x|>28 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered
      |7x| > 28 

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 |7x|

 For the Negative case we'll use -(7x) 

For the Positive case we'll use (7x) 

Step  3  :

Solve the Negative Case

      -(7x) > 28 

     Multiply
      -7x > 28 

     Divide both sides by 7
      -x > 4 

     Multiply both sides by (-1)
     Remember to flip the inequality sign
      x < -4 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (7x) > 28 

     Divide both sides by 7
      x > 4 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

  x < -4
  x > 4

Solutions in Interval Notation

    (-∞,-4)
 
    (4,+∞) 

Solutions on the Number Line

Two solutions were found :

1.   x > 4
2.   x < -4