You want g (u), so we have to solve this equation for v.
[tex]8v+1=-12u+3\qquad\text{subtract 1 from both sides}\\\\8v=-12u+2\qquad\text{divide both sides by 8}\\\\v=\dfrac{2-12u}{8}\\\\v=\dfrac{2:2-12u:2}{8:2}\\\\v=\dfrac{1-6u}{4}\\\\v=\dfrac{1}{4}-\dfrac{6}{4}u\\\\v=\dfrac{1}{4}-\dfrac{6:2}{4:2}u\\\\v=\dfrac{1}{4}-\dfrac{3}{2}u\\\\Answer:\ \boxed{g(u)=\dfrac{1}{4}-\dfrac{3}{2}u}[/tex]
