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

1 Answer
demathgirl
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

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