Solution - Absolute value equations

Absolute Value Equation entered :

      3|-8x|+8=80 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      3|-8x|+8 = 80 

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

      3|-8x| = 72 

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|-8x|

 For the Negative case we'll use -3(-8x) 

For the Positive case we'll use 3(-8x) 

Step  3  :

Solve the Negative Case

      -3(-8x) = 72 

     Multiply
      24x = 72 

     Divide both sides by 24
      x = 3 

Step  4  :

Solve the Positive Case

      3(-8x) = 72 

     Multiply
      -24x = 72 

     Divide both sides by 24
      -x = 3 

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

Step  5  :

Wrap up the solution

 x=3
 x=-3

Solutions on the Number Line

Two solutions were found :

1.  x=-3
   
2.  x=3