[tex]6+\frac{v}{-8}=\frac{4}{7}\ \ \ \ \ \ |subtract\ 6\ from\ both\ sides\\\\\frac{v}{-8}=-5\frac{3}{7}\\\\\frac{v}{-8}=-\frac{5\times7+3}{7}\\\\\frac{v}{-8}=-\frac{38}{7}\ \ \ \ \ \ |multiply\ both\ sides\ by\ (-8)\\\\v=\frac{304}{7}\\\\\boxed{v=43\frac{3}{7}}[/tex]
[tex]if\\\\\frac{6+v}{-8}=\frac{4}{7}\ \ \ \ \ \ |cross\ multiply\\\\7(6+v)=-8\times4\\\\42+7v=-32\ \ \ \ \ |subtract\ 42\ from\ both\ sides\\\\7v=-74\ \ \ \ \ \ |divide\ both\ sides\ by\ 7\\\\v=-\frac{74}{7}\\\\\boxed{v=-10\frac{4}{7}}[/tex]
