First, multiply each side of the equation by #color(red)(8)# to eliminate the fractions to make working with the equation easier and keep the equation balanced:
#color(red)(8) xx (7x + 1/-8) = color(red)(8) xx (x - 3/4)#
#(color(red)(8) xx 7x) + (color(red)(8) xx 1/-8) = (color(red)(8) xx x) - (color(red)(8) xx 3/4)#
#56x + 8/-8 = 8x - 24/4#
#56x - 1 = 8x - 6#
Next, subtract #color(red)(8x)# and add #color(blue)(1)# to each side of the equation to isolate the #x# terms and keep the equation balanced:
#56x - 1 - color(red)(8x) + color(blue)(1) = 8x - 6 - color(red)(8x) + color(blue)(1)#
#56x - color(red)(8x) - 1 + color(blue)(1) = 8x - color(red)(8x) - 6 + color(blue)(1)#
#(56 - 8)x - 0 = 0 - 5#
#48x = -5#
Now, divide each side of the equation by #color(red)(48)# to solve for #x# while keeping the equation balanced:
#(48x)/color(red)(48) = -5/color(red)(48)#
#(color(red)(cancel(color(black)(48)))x)/cancel(color(red)(48)) = -5/48#
#x = -5/48#
