First, multiply each side of the equation by #color(red)(20)# (the LCD of both fractions) to eliminate the fractions while keeping the equation balanced:
#color(red)(20)(x - 3/4) = color(red)(20) xx -9/10#
#(color(red)(20) xx x) - (color(red)(20) xx 3/4) = cancel(color(red)(20))2 xx -9/color(red)(cancel(color(black)(10)))#
#20x - (cancel(color(red)(20))5 xx 3/color(red)(cancel(color(black)(4)))) = -18#
#20x - 15 = -18#
Next, add #color(red)(15)# to each side of the equation to isolate the #x# term while keeping the equation balanced:
#20x - 15 + color(red)(15) = -18 + color(red)(15)#
#20x - 0 = -3#
#20x = -3#
Now, divide each side of the equation by #color(red)(20)# to solve for #x# while keeping the equation balanced:
#(20x)/color(red)(20) = -3/color(red)(20)#
#(color(red)(cancel(color(black)(20)))x)/cancel(color(red)(20)) = -3/20#
#x = -3/20#
