Solve for y:
(3 y)/8-5/6 = y/3-5/2
Put each term in (3 y)/8-5/6 over the common denominator 24: (3 y)/8-5/6 = (9 y)/24-(20)/24:
(9 y)/24-(20)/24 = y/3-5/2
(9 y)/24-(20)/24 = (9 y-20)/24:
(9 y-20)/24 = y/3-5/2
Put each term in y/3-5/2 over the common denominator 6: y/3-5/2 = (2 y)/6-(15)/6:
(9 y-20)/24 = (2 y)/6-(15)/6
(2 y)/6-(15)/6 = (2 y-15)/6:
(9 y-20)/24 = (2 y-15)/6
Multiply both sides by 24:
(24 (9 y-20))/24 = (24 (2 y-15))/6
(24 (9 y-20))/24 = 24/24×(9 y-20) = 9 y-20:
9 y-20 = (24 (2 y-15))/6
24/6 = (6×4)/6 = 4:
9 y-20 = 4 (2 y-15)
Expand out terms of the right hand side:
9 y-20 = 8 y-60
Subtract 8 y from both sides:
(9 y-8 y)-20 = (8 y-8 y)-60
9 y-8 y = y:
y-20 = (8 y-8 y)-60
8 y-8 y = 0:
y-20 = -60
Add 20 to both sides:
y+(20-20) = 20-60
20-20 = 0:
y = 20-60
20-60 = -40:
Answer: |y = -40
