First, multiply each side of the equation by #color(red)(8)# to clear the fractions while keeping the equation balanced:

#color(red)(8)(1/2 - 5/8x) = color(red)(8)(7/8x + 7/2)#

#(color(red)(8) xx 1/2) - (color(red)(8) xx 5/8x) = (color(red)(8) xx 7/8x) + (color(red)(8) xx 7/2)#

#color(red)(8)/2 - (cancel(color(red)(8)) xx 5/color(red)(cancel(color(black)(8)))x) = (cancel(color(red)(8)) xx 7/color(red)(cancel(color(black)(8)))x) + 56/2#

#4 - 5x = 7x + 28#

Next, add #color(red)(5x)# and subtract #color(blue)(28)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#4 - color(blue)(28) - 5x + color(red)(5x) = 7x + color(red)(5x) + 28 - color(blue)(28)#

#-24 - 0 = (7 + color(red)(5))x + 0#

#-24 = 12x#

Now, divide each side of the equation by #color(red)(12)# to solve for #x# while keeping the equation balanced:

#-24/color(red)(12) = (12x)/color(red)(12)#

#-2 = (color(red)(cancel(color(black)(12)))x)/cancel(color(red)(12))#

#-2 = x#

#x = -2#