Simplify the following:
5 t + (t - 3) - ((7 t + 5) - (8 - 3 t))
-(8 - 3 t) = 3 t - 8:
5 t + t - 3 - (3 t - 8 + 7 t + 5)
Grouping like terms, 7 t + 3 t - 8 + 5 = (7 t + 3 t) + (5 - 8):
5 t + t - 3 - ((7 t + 3 t) + (5 - 8))
7 t + 3 t = 10 t:
5 t + t - 3 - (10 t + (5 - 8))
5 - 8 = -3:
5 t + t - 3 - (10 t + -3)
Grouping like terms, 5 t + t - 3 - (10 t - 3) = -(10 t - 3) + (5 t + t) - 3:
-(10 t - 3) + (5 t + t) - 3
5 t + t = 6 t:
-(10 t - 3) + 6 t - 3
-(10 t - 3) = 3 - 10 t:
3 - 10 t + 6 t - 3
Grouping like terms, 3 - 10 t + 6 t - 3 = (3 - 3) + (6 t - 10 t):
(3 - 3) + (6 t - 10 t)
6 t - 10 t = -4 t:
-4 t + (3 - 3)
3 - 3 = 0:
Answer: -4 t
