Answer
$x=\left\{ -3,-5 \right\}$
Work Step by Step
Using the properties of equality, the given equation, $
|x+4|+1=2
,$ is equivalent to
\begin{array}{l}\require{cancel}
|x+4|=2-1
\\\\
|x+4|=1
.\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}
x+4=1 \text{ OR } x+4=-1
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x+4=1
\\\\
x=1-4
\\\\
x=-3
\\\\\text{ OR }\\\\
x+4=-1
\\\\
x=-1-4
\\\\
x=-5
.\end{array}
Hence, the solutions are $
x=\left\{ -3,-5 \right\}
.$
