Answer
The solution set is $(-\infty,-3]\cup[3,\infty)$
Work Step by Step
$x^2\ge9\hspace{0.7cm}{\color{blue}{\text{Given equation}}}$
$\Rightarrow x^2-9\ge0$
$\Rightarrow (x-3)(x+3)\ge0\hspace{0.7cm}{\color{blue}{\text{Factor}}}$
The factors of the left-hand side are $x-3$ and $x+3$.
These factors are zero when $x=3$ and $x=-3$.
These numbers divide the real line into the intervals
$(-\infty,-3),(-3,3),(3,\infty)$
From the diagram and hence the inequality involves $\ge$, the endpoints of the intervals satisfy the inequality.
The solution set is $(-\infty,-3]\cup[3,\infty)$
