I guess this is a geometry question where P, T and Q are points and PT and TQ are line segments, but no picture has been provided so we don't know the relationship between the segments which will help us find x. So let's look at some possibilities.T cannot be midway between P and Q because that would give us a negative x and negative lengths for PT and TQ.
If P is midway between Q and T then QP=PT and QT=2PT, so 9x+7=2(7x+3), 9x+7=14x+6, 1=5x, so x=⅕.