Find all values of $t$ such that $\lfloor t\rfloor = 3t + 4/5$. If you find more than one value, then list the values you find in increasing order, separated by commas.

Answer 1

The integers $\lfloor t\rfloor$ and $3t$ differ by at most 1, so $$|\lfloor t\rfloor - (3t + 4/5)| \le 1.$$Since 4/5 is less than 1, the right side of the above inequality is less than 2. We get $$|(3t + 4/5) - \lfloor t\rfloor| < 2.$$To make this absolute value less than 2, $3t$ must be at least $-2$ units away from the nearest integer. The possible values of $t$ are therefore as follows. Since $3t$ ranges from 0 to 3t+4/4 ranges from 0 plus 4/5 to plus 3 plus 4/5, so t ranges from $4/5$ to $19/5$. We now must intersect this interval with the interval $[-2,2]$. This intersection is $\boxed{[4/5,2]}$.