First, group and combine like terms on each side of the inequality:
#-w - 4w + 9 <= w - 21 - w#
#-1w - 4w + 9 <= w - w - 21#
#(-1 - 4)w + 9 <= 0 - 21#
#-5w + 9 <= -21#
Next, subtract #color(red)(9)# from each side of the inequality to isolate the #w# term while keeping the inequality balanced:
#-5w + 9 - color(red)(9) <= -21 - color(red)(9)#
#-5w + 0 <= -30#
#-5w <= -30#
Now, divide each side of the inequality by #color(blue)(-5)# to solve for #w# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we need to reverse the inequality operator:
#(-5w)/color(blue)(-5) color(red)(>=) (-30)/color(blue)(-5)#
#(color(red)(cancel(color(black)(-5)))w)/cancel(color(blue)(-5)) color(red)(>=) 6#
#w >= 6#
