1. The problem involves solving for $x$ given the equation $x = 23$ and other expressions involving $x$. 2. The first expression is $x = \frac{45}{23}$, which is a fraction representing $x$. 3. The next equation is $x - \frac{2}{4} - 3 = x - \frac{4}{5}$. 4. Simplify the fractions: $\frac{2}{4} = \frac{1}{2}$. 5. Rewrite the equation as $x - \frac{1}{2} - 3 = x - \frac{4}{5}$. 6. Combine constants on the left: $-\frac{1}{2} - 3 = -\frac{1}{2} - \frac{6}{2} = -\frac{7}{2}$. 7. So the equation becomes $x - \frac{7}{2} = x - \frac{4}{5}$. 8. Subtract $x$ from both sides: $-\frac{7}{2} = -\frac{4}{5}$. 9. This is a contradiction since $-\frac{7}{2} \neq -\frac{4}{5}$, so no solution from this equation. 10. The other values given for $x$ are $70$, $54$, $61$, and $57$, but no equations relate them. 11. Since the first equation $x=23$ is given, the solution for $x$ is $23$. Final answer: $x = 23$