First, get rid of the fractions by multiplying everything by a number which a multiple of both #2# and #3#, say #6#:

#color(red)(6)xx(-3v-5/2)=color(red)(6)xx(7/2v-4/3)#

Distribute the #6# through the parentheses on both sides

#6xx(-3v)-6xx(5/2)=6xx(7/2v)-6xx(4/3)#

#-18v-3xx5=3xx7v-2xx4#

#-18v-15=21v-8#

Add #18v# to both sides

#-18vcolor(red)(+18v)-15=21vcolor(red)(+18v)-8#

#15=39v-8#

Add #8# to both sides, to the variable #v# "more alone"

#15color(red)(+8)=39v-8color(red)(+8)#

#23=39v#

Divide both sides by #39# to isolate the #v#

#23/color(red)(39)=(cancel(39)v)/color(red)(cancel(39))#

This leaves

#v=23/39#

Because #23# is a prime number, this fraction is reduced to lowest terms.