Critical values of x in this inequality are x=½ and x=-4.
Let y=(2x-1)/(x+4).
First consider x<-4.
y=(-)/(-)=(+) so x<-4 does not satisfy the inequality.
Now consider -4<x<½.
y=(-)/(+)=(-) so -4<x<½ satisfies the inequality.
When x=½, y=0, so -4<x≤½ satisfies the inequality.
Finally consider x>½.
y=(+)/(+)=(+), so x>½ does not satisfy the inequality.
ANSWER: -4<x≤½.