SOLUTION: solve the absolute calue inequality. other than 0, use interval notation to express the solution set and graph the solution set on a number line |2y+6/3|<2

Here are the rules for removing the absolute value bars in an
absolute value inequality of the form 

1.  For cases of the form  where A is 
    a positive number, write this:

                           
                      
    
2.  For cases of the form  where A is a
    positive number, write this:

                           
                      

3.  For cases of the form  where A is a 
    positive number, write this:
             
                 

4.  For cases of the form  where A is a
    positive number, write this:
             
                

Your problem:

 is case 1, so to remove the absolute value symbols,
we write:



Now we multiply all three sides by 3 to clear of the fraction:







Subtract  from all three sides:





Divide all three sides by 2 to solve for y
in the middle:







Mark -6 and 0 with open circles

<--------------o-----------------o------------>
 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  

Now shade between them:

<--------------o=================o------------>
 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4

In interval notation that is written (-6,0)

Edwin