First, multiply each side of the equation by color(red)(36)36 to eliminate the fractions while keeping the equation balanced:
color(red)(36)(2/9w - 1/4) = color(red)(36) xx 5/636(29w−14)=36×56
(color(red)(36) xx 2/9w) - (color(red)(36) xx 1/4) = cancel(color(red)(36))6 xx 5/color(red)(cancel(color(black)(6)))
(cancel(color(red)(36))4 xx 2/color(red)(cancel(color(black)(9)))w) - (cancel(color(red)(36))9 xx 1/color(red)cancel(color(black)(4)))) = 30
8w - 9 = 30
Next, add color(red)(9) to each side of the equation to isolate the w term while keeping the equation balanced:
8w - 9 + color(red)(9) = 30 + color(red)(9)
8w - 0 = 39
8w = 39
Now, divide each side of the equation by color(red)(8) to solve for w while keeping the equation balanced:
(8w)/color(red)(8) = 39/color(red)(8)
(color(red)(cancel(color(black)(8)))w)/cancel(color(red)(8)) = 39/8
w = 39/8