First, expand the terms in parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:
#15x - 1 = color(red)(2)(5x - 2) + 8#
#15x - 1 = (color(red)(2) xx 5x) - (color(red)(2) xx 2) + 8#
#15x - 1 = 10x - 4 + 8#
#15x - 1 = 10x + 4#
Next, add #color(red)(1)# and subtract #color(blue)(10x)# from each side of the equation to isolate the #x# term while keeping the equation balanced:
#-color(blue)(10x) + 15x - 1 + color(red)(1) = -color(blue)(10x) + 10x + 4 + color(red)(1)#
#(-color(blue)(10) + 15)x - 0 = 0 + 5#
#5x = 5#
Now, divide each side of the equation by #color(red)(5)# to solve for #x# while keeping the equation balanced:
#(5x)/color(red)(5) = 5/color(red)(5)#
#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 1#
#x = 1#
