Answer
$x=-18\text{ OR }x=10$
Work Step by Step
Using the properties of equality, the given equation, $
|x+4|+3=17
,$ is equivalent to
\begin{array}{l}\require{cancel}
|x+4|+3-3=17-3
\\
|x+4|=14
.\end{array}
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x+4=14
\\\\\text{OR}\\\\
x+4=-14
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x+4-4=14-4
\\
x=10
\\\\\text{OR}\\\\
x+4-4=-14-4
\\
x=-18
.\end{array}
Hence, $
x=-18\text{ OR }x=10
.$
