$-(x-1)=1-x$
\(\boxed{\text{The solution to the equation is all real numbers}}\)
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 :\(\boxed{\text{The solution to the equation is all real numbers}}\)