First, remove the terms from parenthesis on each side of the equation, the group and combine like terms:
#-9 + 4x - 2 = -5x - 5 + 1#
#4x - 2 - 9 = -5x - 5 + 1#
#4x + (-2 - 9) = -5x + (-5 + 1)#
#4x + (-11) = -5x + (-4)#
#4x - 11 = -5x - 4#
Next, add #color(red)(11)# and #color(blue)(5x)# to each side of the equation to isolate the #x# term while keeping the equation balanced:
#color(blue)(5x) + 4x - 11 + color(red)(11) = color(blue)(5x) - 5x - 4 + color(red)(11)#
#(color(blue)(5) + 4)x - 0 = 0 + 7#
#9x = 7#
Now, divide each side of the equation by #color(red)(9)# to solve for #x# while keeping the equation balanced:
#(9x)/color(red)(9) = 7/color(red)(9)#
#(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = 7/9#
#x = 7/9#
