Answer
$[5, 9]$
Refer to the graph below.
Work Step by Step
Solve each inequality.
\begin{align*}
x-3&\le 6\\
x-3+3&\le6+3\\
x&\le 9
\end{align*}
\begin{align*}
x+2&\ge 7\\
x+2-2&\ge7-2\\
x&\ge 5
\end{align*}
Thus, the given statement is equivalent to:
$$x\le 9 \text{ and } x \ge 5$$
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.
$x\le9$ includes all the real numbers that are less than or equal to $9$.
$x\ge5$ includes all the real numbers that are greater than or equal to $5$.
Note the that numbers common to the two given sets are the numbers that are greater than or equal to $5$ but less than or equal to $9$.
Hence, the solution set is $[5, 9]$.
Graph the solution set by plotting solid dots ar $5$ and $9$, then shading the region between them. (Refer to the graph above.)
