First, add #color(red)(1)# and subtract #color(blue)(5/7w)# from each side of the inequality to isolate the #w# term while keeping the inequality balanced:
#8/7w - color(blue)(5/7w) - 1 + color(red)(1) > 5/7w - color(blue)(5/7w) + color(red)(1) - 2/3#
#(8/7 - color(blue)(5/7))w - 0 > 0 + (3/3 xx color(red)(1)) - 2/3#
#(8 - color(blue)(5))/7w > color(red)(3/3) - 2/3#
#3/7w > (color(red)(3) - 2)/3#
#3/7w > 1/3#
Now, multiply each side of the inequality by #color(red)(7)/color(blue)(3)# to solve for #w# while keeping the inequality balanced:
#color(red)(7)/color(blue)(3) xx 3/7w > color(red)(7)/color(blue)(3) xx 1/3#
#cancel(color(red)(7))/cancel(color(blue)(3)) xx color(blue)(cancel(color(black)(3)))/color(red)(cancel(color(black)(7)))w > (color(red)(7) xx 1)/(color(blue)(3) xx 3)#
#w > 7/9#
