SOLUTION: 1/3 | 2x-1|<1

Multiply both sides by 3 to get the absolute value 
alone on the left:



Now you must learn the two rules for getting rid of
the absolute values in inequalities:

1. If the problem is , to get
rid of the absolute values write that as

       

2. If the problem is , to get
rid of the absolute values write that as

        

Your problem is case 1, so rewrite



as 



We must solve for x in the middle:

Add 1 to all three sides:





Divide all three sides by 2



which simplifies to



or in interval notation (-1,2)

Edwin