Solve $LaTeX: \displaystyle x^{2} - 89\geq 1 - x$

Getting zero on the right hand side and factoring gives $LaTeX: \displaystyle x^{2} + x - 90=0\iff \left(x - 9\right) \left(x + 10\right)=0$ . This gives the critical numbers as $LaTeX: \displaystyle x=9$ and $LaTeX: \displaystyle x=-10$ .

Checking the sign in each region gives the solution $LaTeX: \displaystyle (-\infty, -10 ] \cup [ 9 ,\infty)$ .