#### Answer

$x=\{ -5,6 \}$

#### Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $
|2x-1|=11
,$ is equivalent to
\begin{array}{l}\require{cancel}
2x-1=11 \text{ OR } 2x-1=-11
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2x-1=11
\\\\
2x=11+1
\\\\
2x=12
\\\\
x=\dfrac{12}{2}
\\\\
x=6
\\\\\text{ OR }\\\\
2x-1=-11
\\\\
2x=-11+1
\\\\
2x=-10
\\\\
x=-\dfrac{10}{2}
\\\\
x=-5
.\end{array}
Hence, the solutions are $
x=\{ -5,6 \}
.$