## Solution.

Two real numbers have the same absolute value if and only if they are either equal or opposite numbers. Therefore, it holds that

$$|x-2023|+2022 x=2022-|2023-x| \text { or }|x-2023|+2022 x=-2022+|2023-x| \text {. }$$

Note that $|x-2023|=|2023-x|$. In the first case, we get the equation

$$\begin{aligned} 2|x-2023| & =2022-2022 x, \text { i.e., } \\ |x-2023| & =1011-1011 x \end{aligned}$$

This equation will have a solution if $1011-1011 x \geqslant 0$, i.e., if $x \leqslant 1$. Then we have either

$$\begin{aligned} x-2023 & =1011-1011 x \\ 1012 x & =3034 \\ x & =\frac{3034}{1012}>1, \end{aligned}$$

which is not a solution, or

$$\begin{aligned} x-2023 & =-1011+1011 x \\ -1010 x & =1012 \\ x & =-\frac{1012}{1010}=-\frac{506}{505} \end{aligned}$$

which is a solution.

In the second case, from $|x-2023|+2022 x=-2022+|2023-x|$ we get $2022 x=-2022$, so $x=-1$.

All solutions to the given equation are $x=-\frac{506}{505} \text{ and } x=-1$.