Solution - Absolute value equations

Absolute Value Equation entered :

      7-5|2x+2|=-23 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered
      -5|2x+2|+7 = -23 

Another term is moved / added to the right hand side.
To make the absolute value term positive, both sides are multiplied by (-1).

      5|2x+2| = 30 

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 5|2x+2|

 For the Negative case we'll use -5(2x+2) 

For the Positive case we'll use 5(2x+2) 

Step  3  :

Solve the Negative Case

      -5(2x+2) = 30 

     Multiply
      -10x-10 = 30 

     Rearrange and Add up
      -10x = 40 

     Divide both sides by 10
      -x = 4 

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

Step  4  :

Solve the Positive Case

      5(2x+2) = 30 

     Multiply
      10x+10 = 30 

     Rearrange and Add up
      10x = 20 

     Divide both sides by 10
      x = 2 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=-4
 x=2

Solutions on the Number Line

Two solutions were found :

1.  x=2
   
2.  x=-4