(-2/3)w - 4/9(-2/3) = -4/5
(-2/3)w + 8/27 = -4/5
(-2/3)w = -4/5 -8/27
-4/5 - 8/27 ⇒ (-4/5)(27/27) - (8/27)(5/5) ⇒ -108/135 - 40/135 = (-108-40)/135
= -148/135
(-2/3)w = -148/135
w = -148/135 ÷ -2/3
w = -148/135 * -3/2 = (-148*-3)/(135*2) = 444/270
w = 1 174/270 or 1 29/45
174 ÷ 2 = 87 ÷ 3 = 29
270 ÷ 2 = 135 ÷ 3 = 45
to check: w = 1 29/45 ⇒ ((1*45)+29)/45 = 74/45
(w-4/9)(-2/3) = -4/5
(74/45 - 4/9)(-2/3) = -4/5
(74/45 - (4/9 * 5/5))(-2/3) = -4/5
(74/45 - 20/45)(-2/3) = -4/5
((74-20)/45)(-2/3) = -4/5
(54/45)(-2/3) = -4/5
(54*-2)/(45*3) = -4/5
-108/135 = -4/5
-4/5 = -4/5
-108 ÷ 27 = -4
135 ÷ 27 = 5