Solution - Absolute value inequalities

Absolute Value Inequality entered :

      5-3|x/7|>2 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered
      -3|x/7|+5 > 2 

Another term is moved / added to the right hand side.
To make the absolute value term positive, both sides are multiplied by (-1). This involves switching the direction of the inequality.

      3|x/7| < 3 

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/7|

 For the Negative case we'll use -3(x/7) 

For the Positive case we'll use 3(x/7) 

Step  3  :

Solve the Negative Case

      -3(x/7) < 3 

     Multiply
      -3x/7 < 3 

     Multiply both sides by 7
      -3x < 21 

     Divide both sides by 3
      -x < 7 

     Multiply both sides by (-1)
     Remember to flip the inequality sign
      x > -7 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      3(x/7) < 3 

     Multiply
      3x/7 < 3 

     Multiply both sides by 7
      3x < 21 

     Divide both sides by 3
      x < 7 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

    -7 < x < 7

Solution in Interval Notation

    (-7,7) 

Solution on the Number Line

One solution was found :