First, multiple the entire inequality by #color(red)(18)# (the lowest common denominator of the fractions) to eliminate the fractions and keep the inequality balanced:
#color(red)(18)(1/3x - 1/9) < color(red)(18) xx 1/6#
#(color(red)(18) xx 1/3x) - (color(red)(18) xx 1/9) < 18/6#
#18/3x - 18/9 < 18/6#
#6x - 2 < 3#
Next, add #color(red)(2)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced.
#6x - 2 + color(red)(2) < 3 + color(red)(2)#
#6x - 0 < 5#
#6x < 5#
Now, divide each side of the inequality by #color(red)(6)# to solve for #x# while keeping the inequality balanced:
#(6x)/color(red)(6) < 5/color(red)(6)#
#(color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6)) < 5/6#
#x < 5/6#
