x + 4 = 3x - 8, is assuming D is the midpoint, and therefore ED = DB.
all we know is that D is somewhere in EB.
[tex]\bf E\stackrel{x+4}{\rule[0.35em]{17em}{0.25pt}}D\stackrel{3x-8}{\rule[0.35em]{10em}{0.25pt}}B
\\\\\\
EB=ED+DB\implies EB=(x+4)+(3x-8)\implies EB=4x-4[/tex]
