Problem 6. Name the set of solutions of the inequality

$$
\sqrt{7+x}>5-x
$$
Solution. We construct the graphs of continuous monotonic functions:

$$
f(x)=\sqrt{7+x} \text { and } \varphi(x)=5-x .
$$

The function $f(x)$ is defined on the interval $[-7 ;+\infty)$, is continuous and monotonically increasing. It varies from 0 to $+\infty$. The function $\varphi(x)$ is defined for all real numbers, it monotonically decreases from $+\infty$ to
$-\infty$. Therefore, the equation $\sqrt{7+x}=5-x$ has a unique solution $x_{0}$. It is easy to notice that $x_{0}=2$. Using the graph, we find the answer: $(2 ;+\infty)$.