Answer
$y=\{-1,0\}$
Work Step by Step
Since for any non-negative number $c$, $|x|=c$ implies $x=c \text{ OR } x=-c$, then the values that satisfy the given equation, $
|2y+1|=1
,$ are
\begin{array}{l}\require{cancel}
2y+1=1
\\\\
2y=1-1
\\\\
2y=0
\\\\
y=\dfrac{0}{2}
\\\\
y=0
\\\\\text{ OR }\\
2y+1=-1
\\\\
2y=-1-1
\\\\
2y=-2
\\\\
y=-\dfrac{2}{2}
\\\\
y=-1
.\end{array}
Hence, $
y=\{-1,0\}
.$
