Frequently in cases involving noncompete agreements, the issue arises as to whether an overly broad covenant not to compete will be held to be completely unenforceable, or whether it will be modified to make it enforceable. In some states, if a noncompetition agreement is overly broad, the entire agreement will be unenforceable. In other states, in response to an overly broad covenant not to compete, the court will engage in what is known as "blue penciling," which means that the court will draw a line through the offending portions of the agreement and enforce whatever remains.
In Texas, if a covenant is overly broad, the court will simply not throw it in the garbage can. Moreover, Texas courts are not confined to merely striking through offending portions. Rather, in response to an overly broad covenant not to compete, a Texas court will judicially reform the agreement to make it enforceable.
Thus, if a noncompete agreement contained no geographic restriction, there is a good chance that a Texas court would add a geographic restriction (the court might, for example, hold that the proper geographic restriction consisted of every state in which the employee worked for the employer). Conversely, in a strict blue-pencil-only state, a court would not add a geographic restriction; rather, the lack of any geographic restriction might result in the entire agreement being voided.
Below is a link to a website which attempts to give a state-by-state summary of how courts deal with overly broad covenants not to compete. I certainly have not confirmed the accuracy of the information contained in this website, and it seems to have been drafted in 2009. Nevertheless, it might be a useful resource for you.