Answer
The solution set is $[5, +\infty)$.
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 $2$ and $-x$ on each side to obtain:
$\begin{array}{ccc}
&2x-2+2-x &\ge &3+x+2+(-x)
\\&(2x-x)+(-2+2) &\ge &(x-x)+(3+2)
\\&x &\ge &5
\end{array}$
Thus, the solution set is $[5, +\infty)$.
