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)(x - 1) + 3 = x - color(blue)(3)(x + 1)#

#(color(red)(2) xx x) - (color(red)(2) xx 1) + 3 = x - (color(blue)(3) xx x) - (color(blue)(3) xx 1)#

#2x - 2 + 3 = x - 3x - 3#

#2x + 1 = -2x - 3#

Next, subtract #color(red)(1)# and add #color(blue)(2x)# to each side of the equation to isolate the #x# term while keeping the equation balanced:

#color(blue)(2x) + 2x + 1 - color(red)(1) = color(blue)(2x) - 2x - 3 - color(red)(1)#

#4x + 0 = 0 - 4#

#4x = -4#

Now, divide each side of the equation by #color(red)(4)# to solve for #x# while keeping the equation balanced:

#(4x)/color(red)(4) = -4/color(red)(4)#

#(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = -1#

#x = -1#