Solve $LaTeX: \displaystyle x^{2} - 57\geq 3 - 11 x$

Getting zero on the right hand side and factoring gives $LaTeX: \displaystyle x^{2} + 11 x - 60=0\iff \left(x - 4\right) \left(x + 15\right)=0$ . This gives the critical numbers as $LaTeX: \displaystyle x=4$ and $LaTeX: \displaystyle x=-15$ .

Checking the sign in each region gives the solution $LaTeX: \displaystyle (-\infty, -15 ] \cup [ 4 ,\infty)$ .