Simplify $1-(1+(1-(1+(1-x))))$.
This problem involves a lot of parentheses and nested expressions, so I will start by working from the inside out and simplifying as I go along. First, I notice that $1+(1-x)$ is the same as $2-x$, so I can replace that with a single term. That gives me $1-(1+(1-(2-x)))$. Next, I see that $1-(2-x)$ is the same as $-1+x$, so I can also replace that with a single term. That gives me $1-(1+(-1+x))$. Now, I notice that $1+(-1+x)$ is the same as $x$, so I can simplify that as well. That gives me $1-(x)$. Finally, I see that $1-(x)$ is the same as $1-x$, so I have my final answer. 