$-(x-1)=1-x$

Step 1 ：Multiply the entire equation by -1 to remove the negative sign from the left side of the equation: \(-1 \times [-(x-1) = 1-x]\) which simplifies to \(x-1 = 1-x\).

Step 2 ：Simplify the equation to get \(x = x\).

Step 3 ：The equation simplifies to a tautology (True statement), which means that the equation holds true for all values of x.

Step 4 ：\(\boxed{\text{The solution to the equation is all real numbers}}\)