Task 2. Name the set of solutions to the inequality

$$
|5-x|<|x-2|+|7-2 x| \text {. }
$$
Solution. Transform the given inequality to the form:

$$
|x-2|+|7-2 x|-|5-x|>0
$$

Construct the graph of the function

$$
f(x)=|x-2|+|7-2 x|-|5-x| \text { (Fig. 1). }
$$

To simplify the construction, let's recall the following:

1) The expressions $|x-2|,|7-2 x|,|5-x|$ are equal to zero at the points $2 ; 3.5 ; 5$, respectively.
2) The graphs of each of the functions $y=|x-2|, y=|7-2 x|, y=|5-x|$ are the union of two rays.
3) Therefore, the graph of the function $f(x)$ is a broken line.
4) To construct this broken line, we find the coordinates of its vertices $B, C, D: f(2)=0 ; f(3.5)=0 ; f(5)=6$.

Then we find the value of the function $f(x)$ at some point lying to the left of the point $x=2$, and at a point lying to the right of the point $x=5$. For example, $f(0)=4$ and $f(6)=8$.

It remains only to read the graph of the function $f(x)$ and write the answer: $(-\infty ; 2),(3.5 ;+\infty)$.