Solve $LaTeX: \displaystyle x^{2} + 20\geq - 11 x - 4$

Getting zero on the right hand side and factoring gives $LaTeX: \displaystyle x^{2} + 11 x + 24=0\iff \left(x + 3\right) \left(x + 8\right)=0$ . This gives the critical numbers as $LaTeX: \displaystyle x=-3$ and $LaTeX: \displaystyle x=-8$ .

Checking the sign in each region gives the solution $LaTeX: \displaystyle (-\infty, -8 ] \cup [ -3 ,\infty)$ .