Answer
$[-2,-1)\cup[9,\infty)$
Work Step by Step
1. Move all the items to the right side $f(x)=4+\frac{5}{x+1}-\frac{x}{2}\leq0$
$f(x)=\frac{8x+8+10-x^2-x}{2(x+1)}=-\frac{x^2-7x-18}{2(x+1)}=-\frac{(x-9)(x+2)}{2(x+1)}\leq0$
2. Cut points $-2,-1,9$, make a table as shown.
3. Solutions $[-2,-1)\cup[9,\infty)$
