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) If $a \lt b$, then $a+c \lt b+c$
Use the rule in (2) above by adding 7 on each side to obtain:
$\begin{array}{ccc}
&3x-7+7 &\gt &2+7
\\&3x &\gt &9
\end{array}$
Use rule the rule in (1) above by multiplying $\frac{1}{3}$ on both sides of the inequality to obtain
$\begin{array}{ccc}
&\frac{1}{3}(3x) &\gt &\frac{1}{3}(9)
\\&x &\gt &3
\end{array}$
Thus, the solution set is $(3, +\infty)$.
To graph this on a number line, plot a hollow dot (or a hole) at $3$ and then shade the region to its right.
