Answer
$(-\infty, 4]$
Refer to the graph below.
Work Step by Step
Solve each inequality.
\begin{align*}
3x-4&\le 8\\
3x-4+4&\le 8+4\\
3x&\le 12\\
\frac{3x}{3}&\le\frac{12}{3}\\
x&\le 4
\end{align*}
\begin{align*}
-4x+1&\ge -15\\
-4x+1-1&\ge -15-1\\
-4x&\ge -16\\
\frac{-4x}{-4} &\le \frac{-16}{-4}\\
x&\le 4
\end{align*}
Thus, the given statement is equivalent to:
$$x\le 4 \text{ and } x \le 4$$
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.
$x\le 4$ includes all the real numbers that are less than or equal $4$.
$x\le 4$ includes all the real numbers that are less than or equal $4$.
The two sets are exactly the same,
Hence, the solution set is $(-\infty, 4)$.
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.)