How do you solve # 2/3 v - 6 = 6 - 2/3 v #?

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Answer 1 · 2017-01-25T15:52:58

#v=9#

#2/3v-6=6-2/3v#

#2/3v+2/3v=6+6#

#4/3v=12#

multiply with #3/4#

#3/4*4/3v=3/4*12#

#v=9#

Answer 2 · 2017-01-25T15:56:10

See the entire solution process below:

First, add #color(red)(2/3v)# and #color(blue)(6)# to each side of the equation to isolate the #v# terms and keep the equation balanced:

#2/3v - 6 + color(red)(2/3v) + color(blue)(6) = 6 - 2/3v + color(red)(2/3v) + color(blue)(6)#

#2/3v + color(red)(2/3v) - 6 + color(blue)(6) = 6 + color(blue)(6) - 2/3v + color(red)(2/3v)#

#4/3v - 0 = 12 - 0#

#4/3v = 12#

Now multiply each side of the equation by #color(red)(3/4)# to solve for #v# while keeping the equation balanced:

#color(red)(cancel(3)/cancel(4)) xx color(red)(cancel(color(black)(4)))/color(red)(cancel(color(black)(3)))v = 36/4#

#v = 9#