How do you solve #3/5=6/(x+3)#?

2 Answers
Jun 23, 2018

Answer:

See a solution process below:

Explanation:

Multiply each side of the equation by #color(red)(5)(color(blue)(x + 3))# to eliminate the fractions while keeping the equation balanced:

#color(red)(5)(color(blue)(x + 3)) xx 3/5 = color(red)(5)(color(blue)(x + 3)) xx 6/(x + 3)#

#cancel(color(red)(5))(color(blue)(x + 3)) xx 3/color(red)(cancel(color(black)(5))) = color(red)(5)cancel((color(blue)(x + 3))) xx 6/color(blue)(cancel(color(black)(x + 3)))#

#3(color(blue)(x + 3)) = color(red)(5) xx 6#

#(3 xx color(blue)(x)) + (3 xx color(blue)(3)) = 30#

#3x + 9 = 30#

Next, subtract #color(red)(9)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#3x + 9 - color(red)(9) = 30 - color(red)(9)#

#3x + 0 = 21#

#3x = 21#

Now, divide each side of the equation by #color(red)(3)# to solve for #x# while keeping the equation balanced:

#(3x)/color(red)(3) = 21/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 7#

#x = 7#

Answer:

#x=7#

Explanation:

Since we have two fractions on either side of an equal sign, this designates that we can cross multiply here. So, let's multiply #3# by #x+3# and #5# by #6#.

#3(x+3)# gives us #3x+9# and #5xx6# gives us #30#. Then we just solve:

#3x+9=30#

Subtract #9# from both sides:

#3x=21#

Divide by #3# on both sides:

#x=7#

Hope this helps!