First, expand the terms in parenthesis on each side of the equation by multiplying each term within the parenthesis by the term outside of the parenthesis:
#color(red)(4)(5x + 7) - 3x = color(blue)(3)(4x - 9)#
#(color(red)(4) xx 5x) + (color(red)(4) xx 7) - 3x = (color(blue)(3) xx 4x) - (color(blue)(3) xx 9)#
#20x + 28 - 3x = 12x - 27#
#20x - 3x + 28 = 12x - 27#
#17x + 28 = 12x - 27#
Next, subtract #color(red)(28)# and #color(blue)(12x)# from each side of the equation to isolate the #x# terms while keeping the equation balanced:
#17x + 28 - color(red)(28) - color(blue)(12x) = 12x - 27 - color(red)(28) - color(blue)(12x)#
#17x - color(blue)(12x) + 28 - color(red)(28) = 12x - color(blue)(12x) - 27 - color(red)(28)#
#5x + 0 = 0 - 55#
#5x = -55#
Now, divide each side of the equation by #color(red)(5)# to solve for #x# while keeping the equation balanced:
#(5x)/color(red)(5) = -55/color(red)(5)#
#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -11#
#x = -11#
