Question

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

Answer 1

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