Answer
$x=-\frac{1}{5}$.
Work Step by Step
The given equation is
$\Rightarrow 11x+1=-1+x$
Subtract $1$ from each side.
$\Rightarrow 11x+1-1=-1+x-1$
Simplify.
$\Rightarrow 11x=-2+x$
Subtract $x$ from each side.
$\Rightarrow 11x-x=-2+x-x$
Simplify.
$\Rightarrow 10x=-2$
Divide each side by $10$.
$\Rightarrow \frac{10x}{10}=\frac{-2}{10}$
Simplify.
$\Rightarrow x=-\frac{1}{5}$
Check:-
$\Rightarrow 11(-\frac{1}{5})+1=-1+(-\frac{1}{5})$
$\Rightarrow -\frac{11}{5}+1=-1-\frac{1}{5}$
$\Rightarrow -\frac{11}{5}+\frac{5}{5}=-\frac{5}{5}-\frac{1}{5}$
$\Rightarrow \frac{-11+5}{5}=\frac{-5-1}{5}$
$\Rightarrow \frac{-6}{5}=\frac{-6}{5}$
True.
Hence, the solution is $x=-\frac{1}{5}$.
