First, multiply each side of the equation by #color(red)(16)# to eliminate the fractions while keeping the equation balanced. #color(red)(16)# is the Lowest Common Denominator of all the fractions:
#color(red)(16)(1/8x - 3/4) = color(red)(16)(7/16x + 1/2)#
#(cancel(color(red)(16)) 2 xx 1/color(red)(cancel(color(black)(8)))x) - (cancel(color(red)(16)) 4 xx 3/color(red)(cancel(color(black)(4)))) = (cancel(color(red)(16))
xx 7/color(red)(cancel(color(black)(16)))x) + (cancel(color(red)(16)) 8 xx 1/color(red)(cancel(color(black)(2))))#
#2x - 12 = 7x + 8#
Next, subtract #color(red)(2x)# and #color(blue)(8)# from each side of the equation to isolate the #x# term while keeping the equation balanced:
#-color(red)(2x) + 2x - 12 - color(blue)(8) = -color(red)(2x) + 7x + 8 - color(blue)(8)#
#0 - 20 = (-color(red)(2) + 7)x + 0#
#-20 = 5x#
Now, divide each side of the equation by #color(red)(5)# to solve for #x# while keeping the equation balanced:
#-20/color(red)(5) = (5x)/color(red)(5)#
#-4 = (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5))#
#-4 = x#
#x = -4#
