Answer
$(-\infty, 6]$
Refer to the graph below.
Work Step by Step
Solve each inequality.
\begin{align*}
7x+6&\le 48\\
7x+6-6&\le 48-6\\
7x&\le 42\\
\frac{7x}{7}&\le\frac{42}{7}\\
x&\le 6
\end{align*}
\begin{align*}
-4x&\ge -24\\
\frac{-4x}{-4} &\le \frac{-24}{-4}\\
x&\le 6
\end{align*}
Thus, the given statement is equivalent to:
$$x\le 6 \text{ and } x \le 6$$
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.
$x\le 6$ includes all the real numbers that are less than or equal $6$.
The two sets are exactly the same,
Hence, the solution set is $(-\infty, 6)$.
Graph the solution set by plotting a solid dot at $4$ and then shading the region from $4$ to the left (Refer to the graph above.)