It says here that line KL bisects angle KAT. This means that KAL and LAT have the same angle measures.
Set up the equation 7x + 3 = 6x + 7
We need the coefficients on one side, remember that once you move a coefficient to the other side, it becomes the opposite of what it currently is:
7x - 6x = 7 - 3
x = 4