Answer
$[5, \infty)$
Refer to the graph below.
Work Step by Step
Add $2$ and subtract $x$ to both sides, then combine like terms to obtain
$$
2x - 2 \geq 3 + x \Longrightarrow 2x - 2+2-x \geq 3 + x+2-x \Longrightarrow x\geq 5
.$$
We have $x\geq 5$.
In terms of intervals, $x\in [2,\infty)$.
To graph, plot a solid dot at $x=5 then shade the region to its right.
See the figure below.
