After five months at 4.1 percent, Texas’ seasonally-adjusted unemployment rate registered at 4.0 percent in June, according to the Texas Workforce Commission.Fayette County’s rate (not seasonally adjusted) dropped 0.1 percent from May, to 3.7. Two other surrounding counties – Gonzales and Lavaca – saw the same decrease while three – Bastrop, Caldwell, and Lee – had increases....