First, expand the term in parenthesis on the right side of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:
#5u - 39 > color(red)(-3)(6 - 4u)#
#5u - 39 > (color(red)(-3) xx 6) - (color(red)(-3) xx 4u)#
#5u - 39 > -18 - (-12u)#
#5u - 39 > -18 + 12u#
Next, subtract #color(red)(5u)# and add #color(blue)(18)# to each side of the inequality to isolate the #u# term while keeping the inequality balanced:
#5u - 39 - color(red)(5u) + color(blue)(18) > -18 + 12u - color(red)(5u) + color(blue)(18)#
#5u - color(red)(5u) - 39 + color(blue)(18) > -18 + color(blue)(18) + 12u - color(red)(5u)#
#0 - 21 > 0 + (12 - color(red)(5))u#
#-21 > 7u#
Now, divide each side of the inequality by #color(red)(7)# to solve for #u# while keeping the inequality balanced:
#-21/color(red)(7) > (7u)/color(red)(7)#
#-3 > (color(red)(cancel(color(black)(7)))u)/cancel(color(red)(7))#
#-3 > u#
To state the solution in terms of #u# we can reverse or "flip" the entire inequality:
#u < -3#
