Answer
Refer to the image below for the graph.
Work Step by Step
RECALL:
(1) The Multiplication Property of Inequality states that if a positive number is multiplied to each side of an inequality, the inequality's direction/sense does not change.
Thus, if $a \gt b$ and $c\gt 0$, then $ac \gt bc$.
(2) The addition property of inequalities states that If $a \ge b$, then $a+c \ge b+c$
Use the rule in (2) above by adding $1$ and $-x$ on each side to obtain:
$\begin{array}{ccc}
&3x-1+1+(-x) &\ge &3+x+1+(-x)
\\&(3x-x)+(-1+1) &\ge &(x-x)+(3+1)
\\&2x &\gt &4
\end{array}$
Use the rule in (1) above by multiplying $\frac{1}{2}$ on both sides of the inequality to obtain:
$\begin{array}{ccc}
&\frac{1}{2}(2x) &\ge &\frac{1}{2}(4)
\\&x &\ge &2
\end{array}$
Thus, the solution set is $[2, +\infty)$.
To graph this on a number line, plot a solid dot at $2$, and then shade the region to its right.