Solve $LaTeX: \displaystyle x^{2} + 10\geq 2 - 9 x$

Getting zero on the right hand side and factoring gives $LaTeX: \displaystyle x^{2} + 9 x + 8=0\iff \left(x + 1\right) \left(x + 8\right)=0$ . This gives the critical numbers as $LaTeX: \displaystyle x=-1$ and $LaTeX: \displaystyle x=-8$ .

Checking the sign in each region gives the solution $LaTeX: \displaystyle (-\infty, -8 ] \cup [ -1 ,\infty)$ .