-1/4 (x-8) +1/2 (x+2) =x+3

easiest to get rid of the fractions. Multiply through by 4:

-(x-8) + 2(x+2) = 4(x+3)

-x+8+2x+4 = 4x+12
3x = 0
x=0

check:
-1/4 (-8) + 1/2 (2) = 3
2+1=3
YES!