#### Answer

$x=0$

#### Work Step by Step

Using the properties of equality, the solution to the given equation, $
11=11(x+1)
$, is
\begin{array}{l}
11=11x+11
\\\\
11-11=11x
\\\\
0=11x
\\\\
x=\dfrac{0}{11}
\\\\
x=0
.\end{array}
CHECKING:
\begin{array}{l}
11=11(0+1)
\\\\
11=11(1)
\\\\
11=11
\text{ (TRUE)}
.\end{array}
Hence, the solution is $
x=0
$.