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