Multiply each side of the equation by #color(red)(7)/color(blue)(-2)# to solve for #v# while keeping the equation balanced:
#color(red)(7)/color(blue)(-2) xx (-2)/7v = color(red)(7)/color(blue)(-2)xx 16#
#cancel(color(red)(7))/cancel(color(blue)(-2)) xx color(blue)(cancel(color(black)(-2)))/color(red)(cancel(color(black)(7)))v = color(red)(7)/(-cancel(color(blue)(2))) xx color(blue)(cancel(color(black)(16)))8#
#v = 56/-1#
#v = -56#
To check the solution, substitute #-56# for #v# in the original equation and ensure the left side of the equation calculates to #16#:
#-2/7v = 16# becomes:
#-2/7 * -56 = 16#
#-2/color(red)(cancel(color(black)(7))) * -8color(red)(cancel(color(black)(56))) = 16#
#-2 * -8 = 16#
#16 = 16#
The answer checks out.
