The distance between two points is the absolute value of the coordinates:
[tex] d=(R,S) = |R-S| [/tex]
We know that [tex] R=-8[/tex] and that the distance is 11, so we have
[tex] |-8-S| = 11 [/tex]
An absolute value equals 11 if its content equals 11 or -11:
[tex] -8-S = 11 \iff -S = 19 \iff S = -19 [/tex]
or
[tex] -8-S = -11 \iff -S = -3 \iff S = 3 [/tex]
