First, multiply each side of the equation by #color(red)(14)# to eliminate the fractions while keeping the equation balanced. It will be easier to solve the equation without fractions and #color(red)(14)# is the lowest common denominator for the three fractions:

#color(red)(14)(2x - 4/7) = color(red)(14)(1/2x + 9/14)#

#(color(red)(14)xx 2x) - (color(red)(14)xx 4/7) = (color(red)(14) xx 1/2x) + (color(red)(14)xx 9/14)#

#28x - (cancel(color(red)(14)) 2 xx 4/color(red)(cancel(color(black)(7)))) = (cancel(color(red)(14)) 7 xx 1/color(red)(cancel(color(black)(2)))x) + (cancel(color(red)(14)) xx 9/color(red)(cancel(color(black)(14))))#

#28x - 8 = 7x + 9#

Next, add #color(red)(8)# and subtract #color(blue)(7x)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#28x - 8 + color(red)(8) - color(blue)(7x) = 7x + 9 + color(red)(8) - color(blue)(7x)#

#28x - color(blue)(7x) - 8 + color(red)(8) = 7x - color(blue)(7x) + 9 + color(red)(8)#

#28x - color(blue)(7x) - 8 + color(red)(8) = 7x - color(blue)(7x) + 9 + color(red)(8)#

#21x - 0 = 0 + 17#

#21x = 17#

Now, divide each side of the equation by #color(red)(21)# to solve for #x# while keeping the equation balanced:

#(21x)/color(red)(21) = 17/color(red)(21)#

#(color(red)(cancel(color(black)(21)))x)/cancel(color(red)(21)) = 17/21#

#x = 17/21#