Solution - Absolute value equations

Absolute Value Equation entered :

      |3b+9|-16=5 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |3b+9|-16 = 5 

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

      |3b+9| = 21 

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 |3b+9|

 For the Negative case we'll use -(3b+9) 

For the Positive case we'll use (3b+9) 

Step  3  :

Solve the Negative Case

      -(3b+9) = 21 

     Multiply
      -3b-9 = 21 

     Rearrange and Add up
      -3b = 30 

     Divide both sides by 3
      -b = 10 

     Multiply both sides by (-1)
      b = -10 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (3b+9) = 21 

     Rearrange and Add up
      3b = 12 

     Divide both sides by 3
      b = 4 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 b=-10
 b=4

Solutions on the Number Line

Two solutions were found :

1.  b=4
   
2.  b=-10