2019 AMC 10B Problem 13

The mean is $7+\frac{x}{5}$. If $x<6$, the median is $6$, so $7+\frac{x}{5}=6$ gives the valid value $x=-5$. If $6\le x\le8$, the median is $x$, but $7+\frac{x}{5}=x$ gives $x=\frac{35}{4}$, outside this interval. If $x>8$, the median is $8$, but $7+\frac{x}{5}=8$ gives $x=5$, again outside the required range. Therefore, the only possible $x$ is $-5,$ making the sum $-5.$ Thus, the answer is A .