How do you solve -\frac { u } { 7} = \frac { 5} { 12+ u }?

1 Answer
Jun 11, 2017

u = -7 or -5

Explanation:

-\frac { u } { 7} = \frac { 5} { 12+ u } ?

I would move the negative sign to the seven

\frac { u } {- 7} = \frac { 5} { 12+ u }

Then cross multiply

u(12 + u) = -7 (5)

Solve

12u +u^2 = -35

Move to the -35 to the other side of the question by adding to both sides. This will make one side zero. I would then put the equation into standard form.

u^2 +12u+ 35 =0

Factor it. (if you want to see more details about how to do this step, please leave a comment and i'll be glad to go into more detail.

(u+7)((u+5) =0

So in order to get the product (the answer of a multiplication problem) to be zero. One of the two terms must be equal to zero. that means

u+ 7 = 0 or u +5 = 0

Solve each equal separately
u +7- (7) =0- (7) -> u = -7
u +5 -(5) = 0 - (5) -> u = -5

so u = -7 or -5