Answer :
[tex]R+3\frac{1}{2}=-4\frac{2}{3}\ \ \ \ | subtract\ 3\frac{1}{2}\\\\
R=-4\frac{2}{3}-3\frac{1}{2}\ \ \ | make\ a\ common\ denominator\\\\
R=-4\frac{4}{6}-3\frac{3}{6}\\\\
R=-7\frac{7}{6}=-8\frac{1}{6}\\\\Solution:\ R=-8\frac{1}{6}[/tex]