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