#### Answer

$x=\left\{ 0,7 \right\}
$

#### Work Step by Step

Using the properties of equality, the given equation, $
|2x-7|+4=11
,$ is equivalent to
\begin{array}{l}\require{cancel}
|2x-7|=11-4
\\\\
|2x-7|=7
.\end{array}
Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the equation above is equivalent to
\begin{array}{l}\require{cancel}
2x-7=7 \text{ OR } 2x-7=-7
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2x-7=7
\\\\
2x=7+7
\\\\
2x=14
\\\\
x=\dfrac{14}{2}
\\\\
x=7
\\\\\text{ OR }\\\\
2x-7=-7
\\\\
2x=-7+7
\\\\
2x=0
\\\\
x=\dfrac{0}{2}
\\\\
x=0
.\end{array}
Hence, the solutions are $
x=\left\{ 0,7 \right\}
.$