Express following inequality in interval notation(y-3)/3 > 1/3 - (y-5)/6?

Question

Express following inequality in interval notation(y-3)/3 > 1/3 - (y-5)/6?

Answer 1

(y-3)/3 > 1/3 - (y-5)/6

y/3 - 3/3 > 1/3 - y/6 + 5/6   ...3/3=1 and get a common denom. on right

y/3 - 1 > 2/6 - y/6 + 5/6   ...2/6 + 5/6 = 7/6

y/3 - 1 > 7/6 - y/6   ...add y/6 to both sides

y/3 + y/6 - 1 > 7/6   ...factor out a y on the left

y(1/3 + 1/6) > 7/6 + 1   ...add 1 to both sides & get common denom

y(2/6 + 1/6) > 7/6 + 6/6   ...2/6 + 1/6 = 3/6 and 7/6 + 6/6 = 13/6

y(3/6) > 13/6   ...multiply both sides by 6

3y > 13   ...divide both sides by 3

y > 13/3

(13/3, ∞)

Hope this helps you!