Line tangent to circle 
A circle with a radius of $2$ units has its center at $(0,0)$. A circle with a radius of $7$ units has its center at $(15,0)$. A line tangent to both circles intersects the $x$-axis at $(x,0)$. What is the value of $x$? Express your answer as a common fraction.

My problem with this question is that there are $4$ such tangent lines, so how do I know which one to pick?

Edit: a quick search (using the information in the comments) I get the feeling that this question deals with problem 21 of this 2008 Mathcounts competition. If so, then I must say I don't see what the problem is. The question comes with a diagram. This diagram clearly shows which tangent line we're considering. So then this question is not so poor at all.
Edit 2: If I had been paying attention, I would have noticed that the document in the link, contains the solutions to the problems. Could not find the actual question, so it might still be a quite poorly worded question.

Original answer: The question as mentioned in the OP is poorly worded. There are four lines tangent to both circles. They intersect the $x$-axis in two different points. See this geogebra sketch:

Not that the OP asks, but both points of intesection are fairly easy to find, via similar triangles.
N.B. I feel inclined to add that the intersection with the positive $x$-axis is probably the one the question wants, since it says "Express your answer as a common fraction." This is not someting one would add to the question when the answer is $-6$.
