Solution - Absolute value equations

Absolute Value Equation entered :

      |-3x-1/4|=2 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      |-3x-(1/4)| = 2 

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 |-3x-(1/4)|

 For the Negative case we'll use -(-3x-(1/4)) 

For the Positive case we'll use (-3x-(1/4)) 

Step  3  :

Solve the Negative Case

      -(-3x-(1/4)) = 2 

     Multiply
      3x+(1/4) = 2 

     Rearrange and Add up
      3x = (7/4) 

     Divide both sides by 3
      x = (7/12) 

Step  4  :

Solve the Positive Case

      (-3x-(1/4)) = 2 

     Rearrange and Add up
      -3x = (9/4) 

     Divide both sides by 3
      -x = (3/4) 

     Multiply both sides by (-1)
      x = -(3/4) 
     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=7/12
 x=-3/4

Solutions on the Number Line

Two solutions were found :

1.  x=-3/4
   
2.  x=7/12