Solve $\frac{1}{3} t - 5 < t - 2 \le -3t + 7.$ Give your answer as an interval.
The solution is (6/5, 13/4].
That is not correct. Thank you though.
The answer is 144.
We have two inequalities to solve
(1/3)t - 5 < t - 2 and t - 2 ≤ -3t + 7
add 2 to both sides, add 2, 3t to both sides
subtract 1/3t from both sides
-3 < t - (1/3)t 4t ≤ 9
-3 < (2/3)t t ≤ 9/4
(-3)(3/2) < t
-9/2 < t
So t = ( -9/2 , 9/4 ]
