Answer
$$-5 \lt x \le 6$$
Refer to the graph below.
Work Step by Step
Solve each inequality:
\begin{align*}
7x &\gt -35\\\\
\frac{7x}{7} &\gt \frac{-35}{7}\\\\
x &\gt -5
\end{align*}
$$\text{and}$$
\begin{align*}
5x&\le 30\\\\
\frac{5x}{5} &\le \frac{30}{5}\\\\
x&\le 6
\end{align*}
Graph each inequality to obtain the one in the attached image below.
Since the compound inequality involves the conjunction $\text{AND}$, then the solutions to the inequality are numbers common to both graphs, which are the numbers in the interval $-5 \lt x \le 6$.
