Simplify the given inequality 2|x+1/3|<9 by dividing both sides by 2:
|x+1/3| < 9/2.
Now think of x = -1/3 as the center of the set of numbers that satisfy 2|x+1/3|<9.
Adding 9/2 to this -1/3 gives us the upper limit of this set:
-1/3 + 9/2, or -2/6 + 27/6, or 25/6.
Subtracting 9/2 from this -1/3 gives us the lower limit of this solution set:
-1/3 - 9/2, or -2/6 - 27/6, or -29/6.
The solution set is (-29/6, 25/6). This is the same as (-4 5/6, 4 1/6).
