Answer
$[2, \infty)$
Refer to the graph below.
Work Step by Step
Add $1$ and subtract $x$ to both sides, then combine like terms to obtain
$$
3x-1+1-x\geq 3+x+1-x \Longrightarrow 2x\gt 1 -5\Longrightarrow 2x\geq 4
.$$
Now, by dividing both sides by $2$, we have $x\geq 2$.
In terms of intervals, $x\in [2,\infty)$.
To graph, plot a solid dot at $x=2$, then shade the region to its right.
See the figure below.
