You only need to flip the inequality if you multiply or divide the inequality by a negative number.
-3t + 7 ≥ 9
Subtract both sides by 7.
-3t + 7 - 7 ≥ 9 - 7
-3t ≥ 2
Divide both sides by -3.
-3t / -3 ≥ 2 / -3
t ≤ 2/-3
So, yes, you will need to flip around the inequality sign.
