Solution - Absolute value inequalities

Absolute Value Inequality entered :

      -|2x|<x+3 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered
      -|2x| < x+3 

To make the absolute value term positive, both sides are multiplied by (-1). This involves switching the direction of the inequality.

      |2x| > -x-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 |2x|

 For the Negative case we'll use -(2x) 

For the Positive case we'll use (2x) 

Step  3  :

Solve the Negative Case

      -(2x) > -x-3 

     Multiply
      -2x > -x-3 

     Rearrange and Add up
      -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

      (2x) > -x-3 

     Rearrange and Add up
      3x > -3 

     Divide both sides by 3
      x > -1 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

    -1 < x < 3

Solution in Interval Notation

    (-1,3) 

Solution on the Number Line

One solution was found :