Break down the problem into these 2 equations.
\[-x-1=-2\]
\[-(-x-1)=-2\]
Solve the 1st equation: \(-x-1=-2\).
Add \(1\) to both sides.
\[-x=-2+1\]
Simplify \(-2+1\) to \(-1\).
\[-x=-1\]
Multiply both sides by \(-1\).
\[x=1\]
\[x=1\]
Solve the 2nd equation: \(-(-x-1)=-2\).
Remove parentheses.
\[x+1=-2\]
Subtract \(1\) from both sides.
\[x=-2-1\]
Simplify \(-2-1\) to \(-3\).
\[x=-3\]
\[x=-3\]
Collect all solutions.
\[x=-3,1\]
Check solution
When \(x=-3\), the original equation \(|-x-1|=-2\) does not hold true.We will drop \(x=-3\) from the solution set.
Check solution
When \(x=1\), the original equation \(|-x-1|=-2\) does not hold true.We will drop \(x=1\) from the solution set.
Therefore,
[No Solution]
