How do you solve #10/5=(3v+10)/(v+4)#?

1 Answer
Feb 10, 2017

Answer:

See the entire solution process below:

Explanation:

First, multiply each side of the equation by the common denominator of the two fractions #color(red)(5)color(blue)((v + 4))# to eliminate the fractions and keep the equation balanced:

#color(red)(5)color(blue)((v + 4)) xx 10/5 = color(red)(5)color(blue)((v + 4)) xx (3v + 10)/(v + 4)#

#cancel(color(red)(5))color(blue)((v + 4)) xx 10/color(red)(cancel(color(black)(5))) = color(red)(5)color(blue)(cancel((v + 4))) xx (3v + 10)/color(blue)(cancel(color(black)((v + 4))))#

#10(v + 4) = 5(3v + 10)#

Next, expand the terms in parenthesis:

#(10 xx v) + (10 xx 4) = (5 xx 3v) + (5 xx 10)#

#10v + 40 = 15v + 50#

Then, subtract #color(red)(10v)# and #color(blue)(50)# from each side of the equation to isolate the #v# term while keeping the equation balanced:

#10v - color(red)(10v) + 40 - color(blue)(50) = 15v - color(red)(10v) + 50 - color(blue)(50)#

#0 - 10 = 5v + 0#

#-10 = 5v#

Now, divide each side of the equation by #color(red)(5)# to solve for #v# while keeping the equation balanced:

#-10/color(red)(5) = (5v)/color(red)(5)#

#-2 = (color(red)(cancel(color(black)(5)))v)/cancel(color(red)(5))#

#-2 = v#

#v = -2#