Solution - Absolute value inequalities

Absolute Value Inequality entered :

      |c+12|+3<17 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered
      |c+12|+3 < 17 

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

      |c+12| < 14 

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 |c+12|

 For the Negative case we'll use -(c+12) 

For the Positive case we'll use (c+12) 

Step  3  :

Solve the Negative Case

      -(c+12) < 14 

     Multiply
      -c-12 < 14 

     Rearrange and Add up
      -c < 26 

     Multiply both sides by (-1)
     Remember to flip the inequality sign
      c > -26 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (c+12) < 14 

     Rearrange and Add up
      c < 2 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

    -26 < c < 2

Solution in Interval Notation

    (-26,2) 

Solution on the Number Line

One solution was found :