The inquality can be simplified as x < 0 or x > 0, the graph of this is in the image at the end.
How to graph the solution set?
We want to find the graph of the inequality:
|x| + 3 > 3
Let's isolate the variable, we can subtract 3 in both sides of the equation, so we will get:
|x| + 3 - 3 > 3 - 3
|x| > 0
Now this is trivial, the absolute value is greater than zero for any value except x = 0, so we can write this as:
x < 0 or x > 0, the graph is shown below.