Answer
$y=-7\text{ OR }y=17$
Work Step by Step
Using the properties of equality, the given equation, $
|y-5|-2=10
,$ is equivalent to
\begin{array}{l}\require{cancel}
|y-5|-2+2=10+2
\\
|y-5|=12
.\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}
y-5=12
\\\\\text{OR}\\\\
y-5=-12
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
y-5=12
\\
y-5+5=12+5
\\
y=17
\\\\\text{OR}\\\\
y-5=-12
\\
y-5+5=-12+5
\\
y=-7
.\end{array}
Hence, $
y=-7\text{ OR }y=17
.$
