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

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Answer 1 · 2018-03-04T21:48:41

See a solution process below:

First, expand the terms on each side of the equation by multiiplying each of the terms within parenthesis by the term outside the parenthesis:

#color(red)(-5)(1 - v) = color(blue)(2)(1 + 2v)#

#(color(red)(-5) xx 1) - (color(red)(-5) xx v) = (color(blue)(2) xx 1) + (color(blue)(2) xx 2v)#

#-5 - (-5v) = 2 + 4v#

#-5 + 5v = 2 + 4v#

Now, add #color(red)(5)# and subtract #color(blue)(4v)# from each side of the equation to solve for #v# while keeping the equation balanced:

#-5 + color(red)(5) + 5v - color(blue)(4v) = 2 + color(red)(5) + 4v - color(blue)(4v)#

#0 + (5 - color(blue)(4))v = 7 + 0#

#1v = 7#

#v = 7#