An arithmetic sequence is of the form a, a+d, a+2d, ... in other words, a+(n-1)d. The difference between any two consecutive terms is constant, so:
x-3-(2x-4)=8-2x-(x-3),
x-3-2x+4=8-2x-x+3,
1-x=11-3x,
2x=10, x=5.
The series is 2x-4, x-3, 8-2x=6, 2, -2 where a=6 and d=-4 (Tn=6-4(n-1)).