Answer
$(-3, -1)$
Refer to the graph below.
Work Step by Step
Solve each inequality.
\begin{align*}
-3x&\gt 3\\
\frac{-3x}{-3}&\lt\frac{3}{-3}\\
x&\lt -1
\end{align*}
\begin{align*}
x+3&\gt 0\\
x+3-3&\gt0-3\\
x&\gt -3
\end{align*}
Thus, the given statement is equivalent to:
$$x\lt -1 \text{ and } x \gt -3$$
The conjunction "and" means intersection so find the intersection of the two sets.
Recall:
The intersection of sets $A$ and $B$ is the set that contains the elements that are common to both sets.
$x\lt-1$ includes all the real numbers that are less than $-1$.
$x\gt-3$ includes all the real numbers that are greater than $-3$.
Note the that numbers common to the two given sets are the numbers that are greater than $-3$ but less than $-1$.
Hence, the solution set is $(-3, -1)$.
Graph the solution set by plotting hollow dots at $-3$ and $-1$, then shading the region between them. (Refer to the graph above.)