First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:
#color(red)(2)(9 - x) > 4x + 9#
#(color(red)(2) xx 9) - (color(red)(2) xx x) > 4x + 9#
#18 - 2x > 4x + 9#
Next, add #color(red)(2x)# and subtract #color(blue)(9)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:
#18 - color(blue)(9) - 2x + color(red)(2x) > 4x + color(red)(2x) + 9 - color(blue)(9)#
#9 - 0 > (4 + color(red)(2))x + 0#
#9 > 6x#
Now, divide each side of the inequality by #color(red)(6)# to solve for #x# while keeping the inequality balanced:
#9/color(red)(6) > (6x)/color(red)(6)#
#(3 xx 3)/color(red)(3 xx 2) > (color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6))#
#(color(red)(cancel(color(black)(3))) xx 3)/color(red)(color(black)(cancel(color(red)(3))) xx 2) > x#
#3/2 > x#
We can reverse or "flip: the entire inequality to state the solution in terms of #x#:
#x < 3/2#
