7.3. The real numbers $x_{1}, x_{2}, x_{3}, \ldots, x_{2022}$ satisfy the relations $\frac{x_{1}}{1+x_{1}}=\frac{x_{2}}{2+x_{2}}=\frac{x_{3}}{3+x_{3}}=\cdots=\frac{x_{2022}}{2022+x_{2022}}$ and $\frac{1}{x_{1}}+\frac{2}{x_{2}}+\frac{3}{x_{3}}+\cdots+\frac{2022}{x_{2022}}=1011$. Determine the value of the expression $x_{1}-x_{2}+x_{3}-x_{4}+\cdots+x_{2021}-x_{2022}$.