Start with
[tex]7|r+5|-2=12[/tex]
Add 2 to both sides:
[tex]7|r+5|=14[/tex]
Divide both sides by 7:
[tex]|r+5|=2[/tex]
Which is true if
[tex]r+5=\pm 2[/tex]
If we choose the positive alternative, we have
[tex]r+5=2 \iff r=3[/tex]
Otherwise, we have
[tex]r+5=-2 \iff r=-7[/tex]
