Answer
$(-1, 4)$
Refer to the graph below.
Work Step by Step
Solve each inequality.
\begin{align*}
-3x&\lt 3\\
\frac{-3x}{-3}&\gt\frac{3}{-3}\\
x&\gt -1
\end{align*}
\begin{align*}
x+2&\lt 6\\
x+2-2&\lt6-2\\
x&\lt 4
\end{align*}
Thus, the given statement is equivalent to:
$$x\gt -1 \text{ and } x \lt 4$$
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.
$x\gt-1$ includes all the real numbers that are greater than $-1$.
$x\lt4$ includes all the real numbers that are less than $4$.
Note the that numbers common to the two given sets are the numbers that are greater than $-1$ but less than $4$.
Hence, the solution set is $(-1, 4)$.
Graph the solution set by plotting hollow dots at $-1$ and $4$, then shading the region between them. (Refer to the graph above.)
