First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:
#3x - color(red)(2)(1.4x - 0.5) = x - 1#
#3x - (color(red)(2) xx 1.4x) + (color(red)(2) xx 0.5) = x - 1#
#3x - 2.8x + 1 = x - 1#
We can next combine like terms:
#(3 - 2.8)x + 1 = x - 1#
#0.2x + 1 = x - 1#
Then, add #color(red)(1)# and subtract #color(blue)(0.2x)# from each side of the equation to isolate the #x# while keeping the equation balanced:
#-color(blue)(0.2x) + 0.2x + 1 + color(red)(1) = -color(blue)(0.2x) + x - 1 + color(red)(1)#
#0 + 2 = -color(blue)(0.2x) + 1x - 0#
#2 = (-color(blue)(0.2) + 1)x#
#2 = 0.8x#
Now, divide each side of the equation by #color(red)(0.8)# to solve for #x# while keeping the equation balanced:
#2/color(red)(0.8) = (0.8x)/color(red)(0.8)#
#2.5 = (color(red)(cancel(color(black)(0.8)))x)/cancel(color(red)(0.8))#
#2.5 =x#
#x = 2.5#
