Question

Solve the proportion for the variable given. 4/v+10 - 6/v+6

Answer 1

`The\ domain:\\v+10\\eq0\ \wedge\ v+6\\eq0\\v\\eq-10\ \wedge\ v\\eq-6\\\\(4)/(v+10)=(6)/(v+6)\ \ \ \ \ |\text{cross multiply}\\\\4(v+6)=6(v+10)\ \ \ \ |\text{use distributive property}\\\\(4)(v)+(4)(6)=(6)(v)+(6)(10)\\\\4v+24=6v+60\ \ \ \ \ |\text{subtract 24 from both sides}\\\\4v=6v+36\ \ \ \ |\text{subtract 6v from both sides}\\\\-2v=36\ \ \ \ |\text{divide both sides by (-2)}\\\\\boxed{v=-18}\in D`