The question we have to solve is:
[tex]\frac{5}{3}s=\frac{15}{3}+\frac{3}{2}s-\frac{1}{4}[/tex]To solve this equation, we take all the "s"'s to one side and numbers to the other and simplify:
[tex]\begin{gathered} \frac{5}{3}s=\frac{15}{3}+\frac{3}{2}s-\frac{1}{4} \\ \frac{5}{3}s-\frac{3}{2}s=\frac{15}{3}-\frac{1}{4} \\ \frac{5(2)-3(3)}{6}s=\frac{15(4)-1(3)}{12} \\ \frac{1}{6}s=\frac{57}{12} \\ s=\frac{\frac{57}{12}}{\frac{1}{6}} \end{gathered}[/tex]When we want to divide by a fraction, we mulitply by its reciprocal. So,
[tex]\begin{gathered} s=\frac{\frac{57}{12}}{\frac{1}{6}} \\ s=\frac{57}{12}\times\frac{6}{1} \\ s=\frac{57}{2} \end{gathered}[/tex]