Answer
Set notation :- $\{x|x\gt -\frac{7}{4}\}$.
Interval notation :- $(-\frac{7}{4},\infty)$.
The graph is shown below.
Work Step by Step
Multiply both sides by $3$.
$3\cdot (3x+4)\gt 3\cdot \frac{1}{3}(x-2) $
Simplify.
$9x+12\gt x-2 $
Add $-12-x$ to both sides.
$9x+12-12-x\gt x-2-12-x $
Simplify.
$8x\gt -14 $
Divide both sides by $8$.
$\dfrac{8x}{8}\gt -\dfrac{14}{8} $
Simplify.
$x\gt -\frac{7}{4} $
The solution set is $\{x|x\gt -\frac{7}{4}\}$
or interval notation is $(-\frac{7}{4},\infty)$.
To graph, use an open parenthesis at $-\frac{7}{4}$ and shade the region to its right..
