#### Answer

$[2, 6]$
Refer to the graph below.

#### Work Step by Step

Solve each inequality.
\begin{align*}
x+5&\le 11\\
x+5-5&\le11-5\\
x&\le 6
\end{align*}
\begin{align*}
x-3&\ge -1\\
x-3+3&\ge-1+3\\
x&\ge 2
\end{align*}
Thus, the given statement is equivalent to:
$$x\le 6 \text{ and } x \ge 2$$
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.
$x\le6$ includes all the real numbers that are less than or equal to $6$.
$x\ge2$ includes all the real numbers that are greater than or equal to $2$.
Note the that numbers common to the two given sets are the numbers that are greater than or equal to $2$ but less than or equal to $6$.
Hence, the solution set is $[2, 6]$.
Graph the solution set by plotting solid dots at $2$ and $6$, then shading the region between them. (Refer to the graph above.)