Because #e# is constant on each side of the equation we need to solve:
#1 - 4x = 5x - 7#
First, add #color(red)(4x)# and #color(blue)(7)# to each side of the equation to isolate the #x# term while keeping the equation balanced:
#1 - 4x + color(red)(4x) + color(blue)(7) = 5x - 7 + color(red)(4x) + color(blue)(7)#
#1 + color(blue)(7) - 4x + color(red)(4x) = 5x + color(red)(4x) - 7 + color(blue)(7)#
#8 - 0 = (5 + color(red)(4))x - 0#
#8 = 9x#
Now, divide each side of the equation by #color(red)(9)# to solve for #x# while keeping the equation balanced:
#8/color(red)(9) = (9x)/color(red)(9)#
#8/9 = (color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9))#
#8/9 = x#
#x = 8/9#
