First, multiply each side of the equation by #color(red)(18)# to eliminate the fractions while keeping the equation balanced. Eliminating the fractions up front will make the problem easier to work with and #color(red)(18)# is the least common denominator of the two fractions:

#color(red)(18)((7/9)x - 1/2) = color(red)(18) xx 3#

#(color(red)(18) xx (7/9)x) - (color(red)(18) xx 1/2) = 54#

#(cancel(color(red)(18))2 xx (7/color(red)(cancel(color(black)(9))))x) - (cancel(color(red)(18))9 xx 1/color(red)(cancel(color(black)(2)))) = 54#

#14x - 9 = 54#

Next, add #color(red)(9)# to each side of the equation to isolate the #x# term while keeping the equation balanced:

#14x - 9 + color(red)(9) = 54 + color(red)(9)#

#14x - 0 = 63#

#14x = 63#

Now, divide each side of the equation by #color(red)(14)# to solve for #x# while keeping the equation balanced:

#(14x)/color(red)(14) = 63/color(red)(14)#

#(color(red)(cancel(color(black)(14)))x)/cancel(color(red)(14)) = (7 xx 9)/(7 xx 2)#

#x = (color(red)(cancel(color(black)(7))) xx 9)/(color(red)(cancel(color(black)(7))) xx 2)#

#x = 9/2#