6 t - 2/3 + t/5 = 4 + (2 - t)/3
Solve for t:
(31 t)/5 - 2/3 = (2 - t)/3 + 4
Put each term in (31 t)/5 - 2/3 over the common denominator 15: (31 t)/5 - 2/3 = (93 t)/15 - 10/15:
(93 t)/15 - 10/15 = (2 - t)/3 + 4
(93 t)/15 - 10/15 = (93 t - 10)/15:
1/15 (93 t - 10) = (2 - t)/3 + 4
Put each term in (2 - t)/3 + 4 over the common denominator 3: (2 - t)/3 + 4 = 12/3 + (2 - t)/3:
(93 t - 10)/15 = 12/3 + (2 - t)/3
12/3 + (2 - t)/3 = ((2 - t) + 12)/3:
(93 t - 10)/15 = (-t + 2 + 12)/3
Grouping like terms, -t + 2 + 12 = (12 + 2) - t:
(93 t - 10)/15 = ((12 + 2) - t)/3
279t - 30 =210 - 15t
279t + 15t =210 + 30
294t = 240
t =240 / 294
t =40 / 49
