With these absolute value equations, you just have to try them positive and negative or square them. We won't do any of that here.
We'll just try to solutions. Clearly x=7 works, |7+6|=2(7)-1
-7 doesn't work
-5/3 gives a positive number on the left and a negative one on the right, nope
5/3 doesn't work either.
Choice A.