Chapter 4 Quadratic Functions and Factoring - 4.9 Graph and Solve Quadratic Inequalities - 4.9 Exercises - Skill Practice - Page 304: 34

$x \leq -2$ or $x \geq 5$

Given $2x^2 -6x-9 \geq 11$. Rewrite as: $2x^2 -6x-20 \geq 0$. Then make a table of values: Notice that $2x^2 -6x-20 \geq 0$ when $x \leq -2$ or $x \geq 5$. The solution of the inequality is $x \leq -2$ or $x \geq 5$.