First, multiply both sides of the equation by the lowest common denominator of the three fractions to eliminate the fractions while keeping the equation balanced. The LCD is #7 xx 3 xx 2 = color(red)(42)#

#color(red)(42) xx -3/2 = color(red)(42)(-6/7v - 5/3)#

#color(red)(42) xx -3/2 = (color(red)(42) xx -6/7v) - (color(red)(42) xx 5/3)#

#cancel(color(red)(42)) 21 xx -3/color(red)(cancel(color(black)(2))) = (cancel(color(red)(42)) 6 xx -6/color(red)(cancel(color(black)(7)))v) - (cancel(color(red)(42)) 14 xx 5/color(red)(cancel(color(black)(3))))#

#21 xx -3 = (6 xx -6v) - (14 xx 5)#

#-63 = -36v - 70#

Next, add #color(red)(70)# to each side of the equation to isolate the #v# term while keeping the equation balanced:

#-63 + color(red)(70) = -36v - 70 + color(red)(70)#

#7 = -36v - 0#

#7 = -36v#

Now, divide each side of the equation by #color(red)(-36)# to solve for #v# while keeping the equation balanced:

#7/color(red)(-36) = (-36v)/color(red)(-36)#

#-7/36 = (color(red)(cancel(color(black)(-36)))v)/cancel(color(red)(-36))#

#-7/36 = v#

#v = -7/36#