How do you solve #2( v - 1) = 6v + 3- 2( - 5v - 1)#?

1 Answer
smendyka
Feb 25, 2017

See the entire solution process below:

Explanation:

First, expand the terms within parenthesis on each side of the equation by multiplying each term within parenthesis by the term outside the parenthesis. Be careful to manage the sign of each individual term correctly:

#(2 xx v) - (2 xx 1) = 6v + 3 - (2 xx -5v) - (2 xx -1)#

#2v - 2 = 6v + 3 - (-10v) - (-2)#

#2v - 2 = 6v + 3 + 10v + 2#

Next, group and combine like terms on the right side of the equation:

#2v - 2 = 6v + 10v + 3 + 2#

#2v - 2 = 16v + 5#

Then, subtract #color(red)(2v)# and #color(blue)(5)# from each side of the equation to isolate the #v# term while keeping the equation balanced:

#2v - 2 - color(red)(2v) - color(blue)(5) = 16v + 5 - color(red)(2v) - color(blue)(5)#

#2v - color(red)(2v) - 2 - color(blue)(5) = 16v - color(red)(2v) + 5 - color(blue)(5)#

#0 - 7 = 14v + 0#

#-7 = 14v#

Now, divide each side of the equation by #color(red)(14)# to solve for #v# while keeping the equation balanced:

#-7/color(red)(14) = (14v)/color(red)(14)#

#-1/2 = (color(red)(cancel(color(black)(14)))v)/cancel(color(red)(14))#

#-1/2 = v#

#v = -1/2#

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