First, expand the terms within parenthesis on each side of the equation by multiplying each term inside the parenthesis by the term outside the parenthesis:
#color(red)(2)(3x - 3) + x = color(blue)(5)(2x - 6) - 5x#
#(color(red)(2) xx 3x) - (color(red)(2) xx 3) + x = (color(blue)(5) xx 2x) - (color(blue)(5) xx 6) - 5x#
#6x - 6 + x = 10x - 30 - 5x#
Next, group and combine like terms on each side of the equation:
#6x + x - 6 = 10x - 5x - 30#
#6x + 1x - 6 = 10x - 5x - 30#
#(6 + 1)x - 6 = (10 - 5)x - 30#
#7x - 6 = 5x - 30#
Then, add #color(red)(6)# and subtract #color(blue)(5x)# from each side of the equation to isolate the #x# term while keeping the equation balanced:
#7x - 6 + color(red)(6) - color(blue)(5x) = 5x - 30 + color(red)(6) - color(blue)(5x)#
#7x - color(blue)(5x) - 6 + color(red)(6) = 5x - color(blue)(5x) - 30 + color(red)(6)#
#(7 - 5)x - 0 = 0 - 24#
#2x = -24#
Now, divide each side of the equation by #color(red)(2)# to solve for #x# while keeping the equation balanced:
#(2x)/color(red)(2) = -24/color(red)(2)#
#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -12#
#x = -12#
